Note: Descriptions are shown in the official language in which they were submitted.
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Interferometric Gravimeter Apparatus and Method
Cross Reference to Related Application
This is a continuation-in-part of the invention described in US patent
application 13/558,138, filed July 25, 2012, for an lnterferometric
Gradiometer
Apparatus and Method, issued as U.S. Patent No. 8,978,565 on March 17, 2015,
made by the inventors hereof and assigned to the assignee hereof.
Field of the Invention
This invention relates to measuring gravity, and more specifically, to a new
and improved gravimeter and method which measures a value of gravity using
multiple light beams which interact with both a freefall test mass and a
reference
test mass while substantially removing or canceling natui iy occurring long
period
seismic disturbances and short period disturbances caused by man or ambient
environmental conditions, thereby improving the accuracy of the gravity
measurement.
Background of the Invention
Gravity is the force of inherent natural attraction between two massive
bodies. The magnitude of the gravitational force is directly related to the
mass of
the bodies and is inversely related to the square of the distance between
centers of
mass of the two attracted bodies.
Gravity is measured as acceleration, g, usually as a vertical vector
component. The freefall acceleration, g, of an object near the surface of the
earth is
given to a first approximation by the gravitational attraction of a point with
the mass
of the entire earth, Me, located at the center of the earth, a distance, Re,
from the
surface of the earth. This nominal gravity value, g = G x Me / Re2, is about
9.8 m/s2.
Thus, the freefall acceleration due to gravity near the earth's surface of an
object
having a small mass compared to the mass of the earth is about 9.8 m/s2. The
common unit of measurement for gravity is the "Galileo" (Gal), which is a unit
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CA 02896010 2015-06-30
acceleration defined as 1 cm/s2. One Gal generally approximates 1/1000 (10-3)
of
the force of gravity at the earth's surface. An instrument used to measure
gravity is
called a "gravimeter."
The most accurate gravimeters are absolute gravimeters. lnterferometric
absolute gravimeters usually use a freefall test mass and a laser or single-
frequency
light beam which reflects from the freefalling test mass. The reflected light
beam is
combined with a reference light beam to develop interference fringes.
Interference
fringes are instances where the amplitude or intensity of the reflected and
reference
light beams add together to create increased intensity, separated by instances
where the two beams cancel or create diminished intensity.
Fringes occur on a periodic basis depending upon the change in the optical
path length of the reflected beam relative to the optical path length of the
reference
beam. One fringe occurs whenever the optical path difference between the
reflected and reference beams changes by the wavelength of the light of the
two
beams. The path length of the reflected beam changes as it is reflected from
the
freefalling test mass, and that change in path length is directly related to
the
acceleration of the test mass caused by gravity. The fringes taken together as
a set
comprise a record of the distance that the freely falling body moves, and that
distance is directly related to the gravity or acceleration of the freefall
test mass.
The use of optical fringe interferometry to measure gravity is well known. US
patent
5,351,122 describes an example of such a gravimeter.
A gravimeter is subject to naturally-occurring and man-made disturbances,
such as seismic noise, mechanical vibrations and other physical perturbations.
The
disturbances cause minute changes in the path lengths of the reflected and
reference light beams in an interferometric gravimeter. When the reflected and
reference light beams are combined, the resulting fringes include information
generated by the disturbances and not by gravity. Consequently, the accuracy
of
the gravity measurement suffers due to the errors introduced by the
disturbances.
Natural seismic noise is a naturally-occurring physical disturbance which is
particularly troublesome in interferometric gravimeters. Natural seismic noise
is the
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natural up-and-down movement of the earth surface at an oscillatory period of
about
3 to 6 seconds. The frequency of seismic noise is comparable to the typical
frequency of ocean waves. Natural seismic noise typically creates vertical
movement of about one micron (1 p) at the earth surface. While a one micron
vertical movement of the earth surface cannot be sensed humanly, it is a very
significant disturbance in an interferometric gravimeter. Typically in an
interferometric gravimeter, fringes occur when the reflected and reference
beam
path lengths differ from one another in increments of one nanometer (1 nm).
Natural seismic noise of about one micron is 1000 times greater than the
typical
path length difference which creates a fringe. Consequently, natural seismic
noise
has the potential to obscure the gravity measurement data with irrelevant and
distracting fringes.
One technique used to eliminate or substantially reduce the effect of natural
seismic noise in an interferometric gravimeter is to include a reflector in
the path of
the reference light beam. The reflector is isolated from the effects of
seismic noise
by suspending it from a conventional long period isolation device. In essence,
the
long period isolation device functions as a spring which has a natural
oscillatory
period which is many times longer than that natural oscillatory period of
seismic
noise. With a long natural oscillatory period, the long period isolation
device
inertially stabilizes and isolates the reflector by disconnecting or
decoupling it from
the effects of seismic noise. In this manner, the reference light beam becomes
substantially unaffected by seismic noise. The reflected light beam interacts
with
the freefalling test mass and is also substantially unaffected by seismic
noise
because the freefall test mass is disconnected or decoupled from the earth
while in
freefall. When the reference and reflected light beams are combined, most of
the
effects of natural seismic noise are eliminated to achieve a more accurate
gravity
measurement. This technique is described in US Patent 5,351,122, and in "A New
Generation of Absolute Gravimeters," Metrologia, vol. 32, pp. 159-180, 1995.
Short period disturbances are difficult to suppress in an interferometric
gravimeter. Short period disturbances, such as mechanical vibrations and other
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types of physical perturbations, are typically man-made and result from
vehicles
moving over the earth surface, or people or animals walking or running on the
earth
surface, or the operation of heavy machinery. Short period disturbances also
arise
from natural ambient environmental conditions, such as wind gusts which impact
the
gravimeter when set up in an outdoor environment or wind guests which impact
trees and other nearby structures which transfer the impact forces as movement
to
the earth surface.
The long period isolation device provides theoretical inertial stabilization
and
isolation of the reference beam reflector against short period external
disturbances.
However, the stabilization and isolation may not be complete from a practical
standpoint. A conventional long period isolation device includes electronic
components and a feedback control mechanism which are intended to respond
principally to long period disturbances. Consequently, the control loop
response of
the long period isolation device may not be fully effective in suppressing and
isolating the reference beam reflector from some types of short period
disturbances.
Short period disturbances have the potential to significantly impact the
freefall
test mass during freefall. Even though the freefall test mass is mechanically
decoupled from the gravimeter and the earth during freefall, short period
disturbances may impact the test mass at the instant when it is released for
freefall,
thereby rotating the test mass while in freefall. Rotation of the freefall
test mass has
the effect of changing the path length of the reflected beam path relative to
the
length of the reference beam path. The change in path length results from the
short
period disturbance which induce rotation of the freefall test mass, not from
the effect
of gravity. Consequently, short period disturbances which rotate the freefall
test
mass during freefall create anomalous fringes which introduce errors into the
gravity
measurement.
The inertial isolation functionality from the long period isolation device
usually
prevents the reflector from rotating in a similar manner or to the same degree
as the
freefall test mass rotates. In those circumstances were the long period
isolation
device is incapable of fully isolating the reference beam reflector from short
period
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disturbances, the movement or rotation of the reference beam reflector will
typically
be different in extent or degree compared to that of the freefall test mass.
Summary of the Invention
This invention eliminates or substantially reduces the adverse effects of both
long period and short period disturbances in a light beam interferometric
gravimeter,
thereby achieving greater accuracy in the measurement of gravity. The adverse
effects of long period disturbances are eliminated by inertially stabilizing
and
isolating a reflector of a reference light beam with a long period isolation
device.
The adverse effects of short period disturbances are eliminated by optically
directing
both the reference and reflected light beams on both a freefall test mass and
the
reference reflector. Both the reflected and reference beams are affected
equally by
the short period disturbances, and those adverse effects are canceled by
common
mode rejection when the reflected and reference light beams are combined to
develop fringes. The adverse effect of any long period disturbance which is
not fully
suppressed by the long period isolation device is also canceled in the same
manner.
A significantly enhanced signal-to-noise ratio is achieved, making the gravity
measurements more accurate and easier to accomplish. These and other features
and benefits are achieved by various aspects of the invention, which are
generally
summarized below.
One aspect of the invention involves a gravimeter for measuring a value of
gravity. The gravimeter comprises a first test mass which is released for
freefall
solely under the influence of gravity, and a second test mass connected to a
long
period isolation device which inertially stabilizes and isolates the second
mass
against long period disturbances. An arrangement of optical elements conduct
first
and second light beams, which have the same initial frequency and a
predetermined
initial phase relationship, through first and second different beam arms. The
first
beam arm directs the first light beam to impinge upon and reflect from both
test
masses during freefall of the first test mass, and the second beam arm directs
the
second light beam to impinge upon and reflect from both test masses during
freefall
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of the first test mass. An interferometric combination of the first and second
light
beams delivered from the first and second beam arms is used in determining the
value of gravity.
Another aspect of the invention involves a method of measuring a value of
gravity. The method comprises freefalling a first test mass solely under the
influence of gravity, inertially stabilizing and isolating a second test mass
from long
period disturbances, directing a first light beam having a predetermined
frequency
into a first beam arm to impinge upon and reflect from both first and second
test
masses during freefall of the first test mass, directing a second light beam
having
the same predetermined frequency and a fixed phase relationship with the first
light
beam into a second beam arm to impinge upon and reflect from both first and
second test masses during freefall of the first test mass, creating fringes by
interferometrically combining the first and second light beams from the first
and
second beam arms after the first and second light beams have impinged upon and
reflected from both test masses during freefall of the first test mass, and
determining
the value of gravity by use of the fringes.
The first and second beam arms are oriented to create equal and opposite
changes in the respective optical path lengths of the first and second beam
arms
during freefall of the first test mass relative to the second test mass, in
response to
the effects of gravity, thereby creating a multiplication or amplification of
the number
of fringe is created to enhance the resolution of the measurement of gravity.
However, in response to distracting external disturbances which adversely
affect
the measurement of gravity, the optical path lengths of the first and second
being
arms are equally affected to result in cancellation of the effects of those
adverse
disturbances when the the first and second light beams are combined
interferometrically to create the fringes. Thus, the present invention
provides the
desirable effect of multiplying the number of fringes created while
simultaneously
suppressing or eliminating the adverse influences from both long and short
period
disturbances, thereby simultaneously enhancing the accuracy of the gravity
measurement.
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Other aspects of the invention involve some or all of the following. Each test
mass has a first reflective surface which is oriented in the same direction as
the
direction of freefall of the first test mass and a second reflective surface
which is
oriented in the opposite direction of freefall of the first test mass. The
first light
beam impinges upon and reflects from the first reflective surface of one test
mass
and the second reflective surface of the other test mass, and the second light
beam
impinges upon and reflects from the second reflective surface of the one test
mass
and the first reflective surface of the other test mass. The first and second
beam
arms are oriented parallel to one another and to the path of freefall movement
of the
first test mass. More than two fringes are created for each wavelength of
distance
that the first test mass moves during freefall relative to the second test
mass. The
value of gravity is derived from counting the number of fringes and the time
of
freefall of the first test mass.
A more complete appreciation of the present invention and its scope may be
obtained from the accompanying drawings, which are briefly summarized below,
from the following detailed description of presently preferred embodiments of
the
invention, and from the appended claims.
Brief Description of the Drawings
Fig. 1 is a generalized block and schematic diagram of an optical
interferometric gravimeter which embodies the invention.
Fig. 2 is a diagram of the gravimeter shown in Fig. 1, showing an
exaggerated amount inadvertent rotation of test masses during a gravity
measurement.
Figs. 3A, 3B and 3C are perspective views of a conventional corner cube
retroreflector of the type used in the gravimeter shown in Fig. 1, each
showing an
incident light beam and a reflected light beam.
Figs. 4A and 4B are perspective and schematic views of test masses of the
type used in the gravimeter shown in Figs. 1 and 2, which each include
retroreflectors of the type shown in Figs. 3A-3C.
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,
Fig. 5 is a flow chart of measuring a value of gravity in accordance with the
invention and by using the gravimeter shown in Fig. 1.
Fig. 6 is a generalized illustration of interference fringes which occur
during
use of the gravimeter shown in Fig. 1.
Detailed Description
An optical light beam interferometric gravimeter 20 which embodies the
present invention is shown in Fig. 1, but aspects of the invention may be
embodied
in other devices and methods used for measuring a characteristic of gravity.
The
gravimeter 20 is used to measure a value of gravity by determining the
distance (D)
that a test mass 22 freefalls solely under the influence of gravity and the
time (t) of
its free fall. The value of gravity (g) is calculated from that information
using the well
known physics equation D = 1/2 g t2.
The movement of the freefalling test mass 22 is relative to a reference test
mass 24 which is positioned substantially stationarily and isolated from
external long
period disturbances, including seismic noise, by a conventional long period
isolation
device 25. The gravity-induced acceleration of the freefalling test mass 22
toward
the reference test mass 24 decreases the relative physical separation distance
between the test masses 22 and 24. An elevator 29, elevator frame 30 and
support
device 31 release the test mass 22 to fall freely solely under the influence
of gravity
and catch the test mass 22 at the end of its freefall. Releasing the test mass
22 for
freefall is accomplished by accelerating the elevator frame 30 and support
device 31
downward at a rate greater than the acceleration of gravity. Catching the test
mass
at the end of its freefall is accomplished by decelerating the elevator frame
30 and
support device 31 at a rate less than the acceleration of gravity and allowing
the
freefalling test mass 22 to settle on the support device 31.
The distance (D) of freefall of the test mass 22 relative to the reference
test
mass 24 is measured by two light beams 26 and 28. The light beams 26 and 28
traverse optical paths referred to herein as beam arms 32 and 34,
respectively. The
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beam arms 32 and 34 are oriented to cause each light beam 26 and 28 to impinge
on and reflect from both the freefall test mass 22 and the reference test mass
24.
The light beams 26 and 28 enter the beam arms 32 and 34 having the same
frequency and a fixed phase relationship. Both light beams 26 and 28 are
derived
from a single constant-frequency light source 36, such as a laser. A single
input
light beam 38 from the light source 36 is conducted through an optical fiber
40 to a
beam splitter 42, and the beam splitter 42 creates the two light beams 26 and
28.
Both light beams 26 and 28 traverse the beam arms 32 and 34 at the speed of
light.
The decreasing relative physical separation of the two test masses during
freefall of the test mass 22 creates a change in the relative lengths of the
beam
arms 32 and 34. The relative change in path length of the beam arms 32 and 34
results in a change in the relative phase relationship of the light beams 26
and 28
when they exit the beam arms 32 and 34. The phase change occurs because the
light beam 26 and 28 traverse different distances in the relatively changed
path
lengths of the beam arms 32 and 34.
After traversing the relatively changed length beam arms 32 and 34, the light
beams 26 and 28 are combined in a beam combiner 44 into a single output light
beam 46. The relatively changed phase relationship of the combined light beams
26 and 28 creates well-known optical fringes 60 (Fig. 6) in the output light
beam 46.
The number of fringes 60 which occur during that time (t) of freefall of the
test mass
22 establishes the distance (D) that the test mass 22 moves during the time of
freefall.
The output light beam 46 containing the fringes 60 is conducted by an optical
fiber 48 to a conventional detector 50. The detector 50 generates signals
which
correspond to characteristics of the output light beam 46, including signals
which
correspond to the interference fringes. A controller/processor 52 responds to
the
fringe signals from the detector 50 and determines the value of gravity from
the
number of fringe signals, the time of freefall and the initial frequency of
the light
beams 26 and 28, by executing well known interferometric analysis and
processing
algorithms.
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A vacuum chamber 27 within a housing 80 of the gravimeter 20 provides an
environment which is as close as possible to a perfect vacuum. The near-
perfect
vacuum eliminates as many gas molecules as possible from within the chamber
27.
By eliminating as many gas molecules as possible, drag on the freefalling test
mass
22 is diminished, thereby enhancing the accuracy of the gravity measurement by
minimizing the adverse influence of drag on the freefall test mass 22.
Isolating and stabilizing the reference test mass 24 with the long period
isolation device 25 prevents long period seismic noise or other external long.
disturbances from changing the optical path length of the light beams 26 and
28 by
moving the reference test mass 24. Any such change in path length would
adversely affect the measurement of gravity, since the change in path length
does
not result from the effect of gravity on the freefall test mass 22 but instead
results
from the external disturbance. Without isolating and stabilizing the reference
test
mass 24, an accurate measurement of gravity is impossible or very difficult to
achieve.
To provide an effective level of inertial stabilization and isolation of the
reference test mass 24, the period of the natural frequency response of the
long
period isolation device 25 should be about 10-20 times or more longer than the
typical period of seismic noise. Although the long period isolation device 25
is
shown schematically in Fig. 1 as a spring, in actuality the device 25 is more
complex
with multiple springs, sensors, feedback controllers and a number of other
active
electronic components, as is well known. Seismic noise usually has no effect
on the
test mass 22 because it is decoupled or disconnected from the effects of
seismic
noise when in freefall. Furthermore, the frequency of seismic noise is so low
that it
has no significant capability of rotating the test mass 22 at the instant when
the test
mass 22 is released for freefall, as compared to short period disturbances
which do
have the capability of rotating the test mass 22 at the instant of release for
freefall,
as discussed below.
In addition to preventing or greatly diminishing the effects of the long
period
disturbances, the gravimeter 20 also prevents or greatly diminishes the
effects of
CA 02896010 2015-06-30
short period disturbances. Short period disturbances are random vibrations and
perturbations which are man-made or which arise from natural causes such as
wind
gusts. Short period disturbances may result from natural and random variations
in
the frequency of the laser light source 36.
Short period disturbances have a significant adverse influence on the
freefalling test mass 22. Short period perturbations or vibrations of the
housing 80
typically impact the test mass 22 at the instant when it is released into
freefall, and
the impact causes random rotation of the test mass 22 during freefall. This is
illustrated in exaggerated form in Fig. 2, where the upper test mass 22 is
shown
rotated clockwise by the effect of a short period disturbance. Rotation of the
test
mass 22 during freefall changes the path length of a light beam which reflects
from
the rotating test mass. Since the change in path length is not the result of
gravity,
rotation of the test mass creates erroneous information and compromises the
accuracy of the gravity measurement.
The relatively long period of the long period isolation device 25 provides
some level of inertial stabilization and isolation of the reference test mass
24 against
short period external disturbances. However, the feedback control system of
the
long period isolation device 25 is intended to respond principally to long
period
disturbances. Consequently, the control loop response of the long period
isolation
device 25 may not be fully effective in suppressing and isolating some effects
of
short period disturbances.
To the extent that the long period isolation device 25 does not fully protect
the reference test mass 24 against short period disturbances, the reference
test
mass 24 may also rotate slightly in response to short period disturbances. The
extent of rotation of the reference test mass 24, if any at all, will usually
be
considerably less than that of the freefall test mass 22. For purposes of
illustration
in Fig. 2, the amount of rotation of the reference test mass 24 is shown as
counterclockwise and in greatly exaggerated form. Thus, the random effect of
short
period disturbances may rotate both test masses in the same or different
directions,
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or rotate one test mass but not the other, or rotate one test mass to a
different
relative degree than the other test mass is rotated.
By arranging the beam arms 32 and 34 to impinge each light beam 26 and 28
on an upward facing retroreflector 72a or 72c of one test mass 22 or 24 and a
downward facing retroreflector 72b or 72d of the other test mass 22 or 24, as
described below, the rotation of either or both test masses 22 and 24 creates
equal
changes in path lengths of both light beams 26 and 28. For example, the beam
arm
32 increases in length while the beam arm 34 also increases in length by an
equal
amount, and vice versa. When the light beams 26 and 28 are combined in the
beam combiner 44 to form the output beam 46, the effects of the equal changes
in
path length are canceled by common mode rejection. Accordingly, the
arrangement
of the beam arms 32 and 34, and the optical elements used in those beam arms
to
direct the light beams 26 and 28, has the advantageous effect of substantially
eliminating the effect of short period disturbances on the measurement of
gravity
obtained from the gravimeter 20. To the extent that the disturbances are not
fully
suppressed by the long period isolation device 25, those disturbances are also
suppressed by the arrangement of the beam arms 32 and 34 and the optical
elements used in those beam arms to direct the light beams 26 and 28. The
accuracy of the gravity measurement is thereby significantly enhanced. The
details
of the beam arms 32 and 34, the test masses 22 and 24 and the optical elements
of
the beam arms which advantageously eliminate the effects of disturbances are
discussed below.
The beam arms 32 and 34 include four conventional corner cube
retroreflectors 70a-70d positioned within the vacuum chamber 27. The
retroreflectors 70a, 70b and 70c are fixed in position, and the retroreflector
70d is
adjustable in position. The test masses 22 and 24 each include one upward
facing
retroreflector 72a and 72c and one downward facing retroreflector 72b and 72d,
respectively. The downward facing retroreflectors 72b and 72d face in the same
direction that the test mass 22 freefalls, and the upward facing
retroreflectors 72a
and 72c face in the opposite direction from the direction that the test mass
22
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freefalls. The retroreflectors 72a, 72b and 72c, 72d are connected to and are
a part
of the test masses 22 and 24, respectively.
The light beams 26 and 28 each reflect from one upward facing retroreflector
of one test mass 22 or 24 and one downward facing retroreflector of the other
test
mass 24 or 22. Specifically, the light beam 26 in the beam path 32 impinges
upon
and reflects from the upward facing retroreflector 72c of the reference test
mass 24
and the downward facing retroreflector 72b of the freefall test mass 22, and
the light
beam 28 in the beam path 34 impinges upon and reflects from the downward
facing
retroreflector 72d of the reference test mass 24 and the upward facing
retroreflector
72a of the freefall test mass 22.
The interaction of each light beam 26 and 28 in each beam arm 32 and 34
with the upward facing retroreflector of one test mass and the downward facing
retroreflector of the other test mass has the effect of eliminating the
adverse effects
of disturbances. When either one or both of the test masses 22 and 24 rotate
during freefall, as shown in Fig. 2, the lengths of both beam arms 32 and 34
change
by the same amount, since the rotation of one or both test masses changes the
length of both beam arms 32 and 34 by the same amount. Consequently the
relative length relationship of the beam arms 32 and 34 is unaffected by
rotation of
one or both of the test masses during freefall caused by short period
disturbances.
Since the lengths of the beam arms 32 and 34 change by the same amount
when the test masses 22 and 24 rotate, interferometrically combining the light
beams 26 and 28 eliminates the adverse effect of the equal path length changes
due to common mode rejection. Consequently, the adverse effects of rotation of
one or both of the test masses on the measurement of gravity is eliminated.
The
gravity measurement available from the gravimeter 20 is substantially free of
errors
arising from both short period disturbances as well as from long period
disturbances.
The beneficial effect of eliminating or substantially reducing the adverse
effects of
short and long period disturbances by reflecting both light beams 26 and 28
from
both test masses 22 and 24 is understood from the details of the beam arms 32
and
34.
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_
The beam arms 32 and 34 include five segments 74a-74e and 76a-76e,
respectively, all of which extend in sequence from the beam splitter 42 to the
beam
combiner 44. The beam splitter 42 delivers the light beam 26 into the first
segment
74a of the beam arm 32. The light beam 26 in the first segment 74a impinges
upon
the retroreflector 70a and reflects into the second segment 74b of the beam
arm 32.
Light from the second segment 74b impinges upon the upward facing
retroreflector
72c of the reference test mass 24 and reflects into the third segment 74c of
the
beam arm 32. Light from the third segment 74c impinges upon the downward
facing
retroreflector 72b of the freefall test mass 22 and reflects into the fourth
segment
74d of the beam arm 32. Light from the fourth segment 74b impinges upon the
retroreflector 70b and reflects into the fifth segment 74e of the beam arm 32
leading
to the beam combiner 44.
The beam splitter 42 delivers the light beam 28 into the first segment 76a of
the beam arm 34. The light beam 28 in the first segment 76a impinges upon the
downward facing retroreflector 72d of the reference test mass 24 and reflects
into
the second segment 76b of the beam arm 34. Light from the second segment 76b
impinges upon the retroreflector 70c and reflects into the third segment 76c
of the
beam arm 34. Light from the third segment 76c impinges upon the retroreflector
70d and reflects into the fourth segment 76d of the beam arm 34. Light from
the
fourth segment 76d impinges upon the upward facing retroreflector 72a of the
freefall test mass 22 and reflects into the fifth segment 74e of the beam arm
34
leading to the beam combiner 44.
The length of the beam arms 32 and 34 is equal at one point during the
freefall of the test mass 22, such as at the point where the test mass 22 is
released
to fall freely. Establishing this equality in path lengths assures that the
disturbances
affect both beam arms 32 and 34 equally, and allow the effect of gravity on
the
freefall test mass 22 to create the difference in path lengths. Equal lengths
of the
beam arms 32 and 34 are achieved by adjusting the vertical position of the
retroreflector 70d in the beam arm 34, as shown in Fig. 1. The position of the
retroreflector 70d is adjusted by manipulation of an adjustment device, such
as a
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micrometer screw 78, which extends through the housing 80 that defines the
vacuum chamber 27. Adjusting the vertical position of the retroreflector 70d
changes the length of the beam arm segments 76c and 76d, and therefore changes
the entire length of the beam arm 34 to make it equal with the length of the
beam
arm 32 at the desired one point.
A multiple frequency light beam, such as a Mercury band limited light beam,
is used as the input light beam 38 for purposes of calibrating the length of
the beam
arms 32 and 34. The test mass 22 is positioned stationarily at the desired
position
where the path lengths are to be equal. So long as the beam arms 32 and 34 are
not equal in length, optical fringes will result in the output light beam 46
in response
to the multiple frequency input light beam. When the length of the beam arm 34
is
adjusted to equal the length of the beam arm 32, by adjusting the position of
the
retroreflector 70d, the output light beam 46 no longer includes any optical
fringes.
The beam arms 32 and 34 are inherently parallel to one another, despite the
movement of the test masses 22 and 24. If the beam arms 32 and 34 were not
parallel to one another, the non-parallel deviation of one of the beam arms
would
cause it to have a different length compared to the other beam arm. Such a
difference in path length would cause the light beam in one beam arm to travel
a
different distance than the light travels in the other beam arm, resulting in
relative
phase changes between the light beams 26 and 28. The phase shifts resulting
from
unequal beam arm lengths would create erroneous interference fringes that
would
lead to errors in determining the value of gravity or other characteristic of
gravity
being measured.
Changes in direction of the light beams 26 and 28 within the beam arms 32
and 34, and the parallel orientation of the beam arms segments 74a-74e and 76a-
76e, are achieved by the retroreflectors 70a-70d and 72a-72d. Use of the
retroreflectors to change the direction of the light beams ensures parallelism
in the
beam arms 32 and 34, thereby maintaining equal path lengths, as understood
from
the following discussion of a single conventional retroreflector 75 shown in
Figs. 3A-
CA 02896010 2015-06-30
3C. The retroreflector 75 exemplifies the characteristics of each
retroreflector 70a-
70d and 72a-72d.
As shown in Fig. 3A, the retroreflector 75 is constructed of glass or other
high-grade transparent optical material. An entry-exit surface 82 and three
mutually
perpendicular wall surfaces 84a-84c are machined or otherwise formed on the
retroreflector 75. The wall surfaces 84a-84c intersect one another
perpendicularly
and define a corner 86 which faces toward the entry-exit surface 82. The wall
surfaces 84a-84c extend at the same angle relative to the entry-axis surface
82.
The wall surfaces 84a-84c are coated with a reflective material (not shown) to
cause
light impinging on the wall surfaces 84a-84c to reflect.
An incident light beam 88 enters the retroreflector 75 through the entry-exit
surface 82 and reflects off of the reflective wall surfaces 84a-84c and then
exits the
retroreflector 75 through the entry-exit surface 82 as a reflected light beam
90. An
optical characteristic of the retroreflector 75, which is created by the
angular
relationship of the reflective wall surfaces 84a-84c, is that the reflected
light beam
90 always projects parallel to the incident light beam 88. This parallel
relationship is
maintained even if the light beam 88 does not impinge on the entry-exit
surface 82
orthogonally. Unlike a mirror, the retroreflector 75 therefore reflects light
back in a
direction parallel to the incident light, regardless of the angle of incidence
of the light
beam 88 with respect to the entry-exit surface 82. This parallel reflection
quality
causes the light beams in the beam arm segments 74b-74e and 76b-76e (Fig. 1)
to
remain parallel with respect to one another and maintain the substantially
equal path
lengths within the vacuum chamber 27 of the gravimeter 20 (Fig. 1), in
response to
disturbances.
Conventional retroreflectors can also be of the open variety. An open
retroreflector is constructed of mirrors or other high-grade reflective
optical material
oriented to form the reflective surfaces 84a, 84b and 84c. An open
retroreflector
can be used in place of each retroreflector described herein. An open
retroreflector
has the effect of not changing the speed of light which occurs when the light
passes
through the changed medium of the optical body of a closed retroreflector.
Using
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,
open retroreflectors causes the speed of light to remain constant throughout
the
entire beam arms 32 and 34, because the light beams do not pass through an
optical body, thereby avoiding any phase or path length differences that might
be
created by conducting the light beams through a different medium.
The parallel surface beam splitter 42 and the parallel surface beam combiner
44 contribute to the parallelism in the beam arms 32 and 34, as understood
from
Figs. 1 and 2. An inherent characteristic of the parallel surfaces of the beam
splitter
42 is that the two light beams 26 and 28 are delivered in a parallel
relationship.
Furthermore, the two light beams 26 and 28 extend in a parallel relationship
with the
input light beam 38. A similar situation exists with respect to the beam
combiner 44,
since the beam combiner 44 is a beam splitter used for the opposite purpose.
The
optical characteristics of the beam combiner 44 are the same as the beam
splitter
42, causing parallel light beams 26 and 28 leaving the parallel beam arms 32
and
34 to be combined accurately in the single output beam 46 while preserving
their
relative phase relationship. The beam combiner 44 delivers the output signal
46 in
parallel relationship to the light beams 26 and 28 delivered from the beam
arms 32
and 34.
The parallel surface beam splitter 42 and the parallel surface beam combiner
44 also contribute to maintaining the previously-described substantial
equality in the
optical path lengths. An inherent characteristic of the parallel surface beam
splitter
42 and beam combiner 44 is that the optical path length of the first light
beam 26 in
the beam splitter 42 added to the optical path length of the first light beam
26 in the
beam combiner 44 is equal to the optical path length of the second light beam
28 in
the beam splitter 42 added to the optical path length of the second light beam
28 in
the beam combiner 44. As a consequence, the light beams passing through the
parallel surface beam splitter 42 and beam combiner 44 retain the substantial
equality in optical path lengths of the beam arms 32 and 34.
Because the light beams 26 and 28 in the beam arms 32 and 34 are parallel
to one another in the vacuum chamber 27, due to the use of the retroreflectors
70a-
70d and 72a-72d, and because output light beam 46 is parallel to the light
beams 26
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and 28 in the beam arms 32 and 34 due to the effect of the parallel surface
beam
combiner 44, a vertical orientation of the test masses 22 and 24 can be
established
by evaluating the vertical orientation of the output light beam 46. When the
output
light beam 46 is vertically oriented, the test masses 22 and 24 will be
vertically
oriented, due to the parallelism of the beam arms 32 and 34. An exact vertical
orientation of the test masses 22 and 24 is essential in establishing an
accurate
value of gravity. If the test masses 22 and 24 are not exactly vertically
oriented, the
gravity measurement will not be accurate. The position of the gravimeter 20 is
adjusted to achieve a precise vertical alignment of the test masses 22 and 24
as
determined by the vertical projection of the output light beam 46.
As an alternative to conducting the input and output light beams 38 and 46
through the optical fibers 40 and 48, mirrors could be used. The optical
fibers 40
and 48 could be eliminated altogether by directly connecting the light source
36 to
the housing 80 and directly injecting the light beam 38 into the gravimeter 20
and by
directly connecting the detector 50 to the housing 80 to directly receive the
output
light beam 46 from the combiner 44.
The manner in which the retroreflectors 72a-72d of the test masses 22 and
24 are effective in creating equal changes in the length of the beam arms 32
and 34
arising from rotation of one or both of the test masses 22 and 24, while
maintaining
the parallel relationship of the impinging and reflected light beams, also
involves
characteristics exemplified by the retroreflector 75 shown in Figs. 3A, 3B and
3C.
The retroreflector 75 has an optical center point 92 which is equidistant from
each of
the reflective wall surfaces 84a-84c. When the retroreflector 75 is rotated
about the
optical center point 92, the path length of the light beam from the point of
incidence
on the entry-exit surface 82 to the point of exit from the entry-exit surface
82
remains constant. Thus, when the retroreflector 75 is rotated about the center
point
92, the path length within the retroreflector remains constant regardless of
the angle
of the incident light beam 88 relative to the entry-exit surface 82. Fig. 3B
illustrates
the situation where the retroreflector 75 has been rotated slightly around the
optical
center point 92, but the length of the light path within the retroreflector 75
remains
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the same as when the incident light beam 88 intersects the entry-exit surface
82
orthogonally (Fig. 3A).
When the retroreflector 75 is rotated about a point 94 which is not coincident
with the optical center point 92, as shown in Fig. 3C, the length of the light
path
within the retroreflector 75 increases in length slightly, and that increase
in length is
related to the amount of angular rotation about the point 94 relative to the
optical
center point 92. For similar changes in angular rotation about points which
have the
same relative relationship to the optical center point 92, the increase in the
length of
the light path within the retroreflector 75 is the same.
The above described properties of retroreflectors are used to advantage in
the test masses 22 and 24, as explained in conjunction with Figs. 4A and 4B.
The
characteristics of the test mass 22 shown in Figs. 4A and 4B apply equally to
the
test mass 24. The retroreflectors 72a and 72b are positioned on the test mass
22
with the entry-exit surfaces 82 facing in opposite directions and extending
parallel to
one another. The corners 86 (Figs. 3A-3C) of the retroreflectors 72a and 72b
are
adjacent to one another. The optical center points 92 of the retroreflectors
72a and
72b are located equidistant from a center of mass point 96 of the test mass
22. The
two optical center points 92 and the center of mass point 96 are located co-
linearly.
The corners 86 (Figs. 3A-3C) are also located coincident with the co-linear
relationship of the two optical center points 92 and the center of mass 96. In
this
configuration, the distance from the center of mass point 96 to the optical
center
point 92 of the retroreflector 72a is equal to the distance from the center of
mass
point 96 to the optical center point 92 of the retroreflector 72b.
The test mass 22 has a physical structure 98 which holds the two
retroreflectors 72a and 72b in place. The physical structure 98 of the test
mass 22
and the two retroreflectors 72a and 72b are balanced so that the center of
mass
point 96 of the test mass 22 is located midway between the two optical center
points
92. Such balancing may be achieved by moving adjustable weights (not shown)
associated with the physical structure 98.
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Locating the center of mass point 96 of the test mass 22 in the manner
described causes the test mass 22 to rotate about the center of mass point 96
if the
test mass 22 rotates while freefalling, as shown in Fig. 4B. Rotation about
the
center of mass point 96 causes the optical center points 92 of both
retroreflectors
72a and 72b to rotate in the same amount and in the same direction relative to
the
center of mass point 96, as shown in Fig. 4B. This similar rotation in the
same
direction causes the parallel light beams which impinge on the retroreflectors
72a
and 72b to change equally in their lengths. Consequently, rotation of the test
mass
22 does not adversely affect the relative length of the beam arms 32 and 34,
because such rotation has the same effect on the length of both beam arms 32
and
34. Since the beam arms 32 and 34 change length by the same amount when the
test mass 22 rotates, the accuracy of measurement is not adversely affected.
If the test mass 22 rotates about any point other than the center of mass
point 96, then the distances over which the respective light beams in the beam
arms
32 and 34 travel will not be equal. However, when the test mass 22 is
freefalling, it
can rotate only about its center of mass point 96, so rotation of the test
mass 22
about some point other than the center of mass point 96 is not possible during
freefall.
The suspension of the reference test mass 24 by the long period isolation
device 25 (Figs. 1 and 2) is applied effectively at the center of mass of the
reference
test mass 24. Suspended in this manner, any rotation of the reference test
mass 24
occurs about its center of gravity in much the same way that rotation of the
freefalling test mass 22 occurs about its center of mass 96 (Figs. 4A and 4B).
Thus,
the suspension effects of the long period isolation device 25 (Fig. 1) causes
any
rotation of the reference test mass 24 to maintain the equal path lengths of
the light
beams 26 and 28 which impinge upon and reflect from the reference test mass in
the same manner that rotation of the freefalling test mass 22 maintains equal
path
lengths of the light beams 26 and 28.
The use of the gravimeter 20 to determine the value of gravity is illustrated
by
the process flow 100 shown in Fig. 5, which is explained in connection with
the
CA 02896010 2015-06-30
components of the gravity meter 20 shown in Fig. 1. The process flow 100
begins at
102. At 104, the freefall test mass 22 is positioned for freefall, by
operation and
movement of the elevator 29, elevator frame 30 and support device 31 under the
control of the controller/processor 52. At 106, the freefall test mass is
released to
freefall solely under the influence of gravity. The freefall test mass is
released for
freefall by accelerating the elevator frame 30 and support device 31 downward
at a
rate greater than the typical value of gravity. Simultaneously with or shortly
after
releasing the test mass 22 for freefall, the controller/processor 52 starts
measuring
or timing the amount of time during which the test mass 22 freefalls, as shown
at
108. The controller/processor 52 recognizes that the test mass 22 is in
freefall
whenever the controller/processor 52 establishes a controlled downward
acceleration of the elevator frame 30 and the support device 31 at a rate
which
exceeds the typical value of gravity.
The fringes created when the test mass 22 free falls are detected at 110.
The output signal 46 containing the fringes is detected by the detector 50 and
processed by the controller/processor 52. After the test mass 22 has been in
freefall for a preselected amount of time, the controller/processor 52 stops
timing the
freefall of the test mass 22, as shown at 112. The number of fringes detected
during the time that the test mass 22 was freefalling is determined by the
controller/processor 52 during the timed freefall. Thereafter, at 114, the
controller/processor 52 reduces the downward acceleration of the elevator
frame 30
and support device 31 and catches the freefall test mass 22 at 114 by allowing
it to
settle onto the support device 31.
It is not necessary that the timed freefall extend from the point at 106 when
the freefall test mass 22 is initially released to freefall to the point at
114 when the
freefall test mass 22 is caught. The time duration of freefall is established
to end at
an arbitrary time period after freefall commences and before the test mass is
caught. During this arbitrary amount of freefall time, the number of fringes
counted
establishes the distance that the test mass 22 moves solely under the
influence of
gravity (as understood from Fig. 6). Counting this number of fringes
establishes the
21
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value of D, and the arbitrary amount of time measured during which freefall
generates the counted number of fringes establishes the value of t, thereby
allowing
the value of gravity to be calculated by the controller/processor 52 (Fig. 1)
according
to the previously described formula D = 1/2 g t2, as shown at 116. Thereafter,
the
process flow 100 terminates at 118.
The end result of executing the process flow 100 is the determination of the
value of gravity. In some practical applications, the process flow 100 is
repeated
several times in succession, and the value of gravity is derived by averaging
the
individual gravity values determined after each execution of the process flow
100.
Averaging the individually-determined gravity values helps eliminate or reduce
anomalous errors.
Many significant improvements result from the present invention. Common
mode rejection cancels or ameliorates the adverse effects of external short
period
disturbances. The common mode rejection results in substantial part because
the
effects of external disturbances on the beam arms 32 and 34 are equal,
allowing
those adverse influences to be rejected or canceled by common mode rejection
when the light beams 26 and 28 are combined interferometrically.
Balancing the test masses 22 and 24 with their centers of mass relative to the
optical center points of their retroreflectors preserves the equal relative
length
relationship of the beam arms 32 and 34, despite rotation of the freefall test
mass
22 that might occur during freefall or the rotation of the reference test mass
24 if it is
not fully isolated from short period disturbances by the long period isolation
device
25. Rotation of one or both of the test masses 22 and 24 does not change the
optical path length of both beam arms 32 and 34. The rotation of the test mass
22
during freefall is not a source of disturbance-induced interference fringes
which
adversely influence and accurate measurement of the gravity value.
The parallel characteristics of the beam arms 32 and 34 are facilitated by the
use of the parallel path optical elements 44, 46, 70a-70d and 72a-72d (Fig. 1)
which
prevent the beam arms 32 or 34 from deviating from the parallel relationship
with
22
CA 02896010 2015-06-30
one another and thereby preserve the equality in length except for the
desirable
changes in relative length which occur during freefall of the test mass 22.
Use of the parallel path optical elements in the gravimeter 20 also greatly
facilitates its assembly and construction. The difficulties associated with
aligning
and maintaining mirrors and other non-inherently parallel path optical
elements is
avoided. Fixing the position of the retroreflectors 70a-70d becomes less
critical
because the retroreflectors create the parallelism in the light beams 26 and
28 even
though the angular orientation of each retroreflector may not be precisely
exact. A
similar situation exists with the retroreflectors 72a-72d attached to the test
masses
22 and 24. Assembling and using the gravimeter 20 under these circumstances is
considerably easier than the tedious and often changeable nature of attempting
to
establish and maintain an exact angle of reflecting mirrors within a
conventional
gravity measuring instrument. Furthermore, the parallel path optical elements
maintain the light beams in their intended parallel paths even during rough
handling
which inevitably occurs during use in an outdoor environment.
The beam arms 32 and 34 also offer the beneficial effect of eliminating
frequency and phase variations in the laser light source 36, which would
otherwise
cause gravity measurement errors comparable to those arising from short period
disturbances. Most laser light sources 36 are subject to slight frequency and
phase
variations during normal operation. In addition, movement of the optical fiber
40 can
also introduce frequency and phase relationships in the input light beam 38
delivered to the beam splitter 42. Even further still, if for some
unanticipated reason,
the beam splitter 42 should move unexpectedly relative to the input light beam
38,
the light beams 26 and 28 will contain the slight frequency and phase
variations.
Any of these circumstances cause the light beams 26 and 28 leaving the beam
splitter 42 to have slight frequency and phase variations.
Any frequency and phase shifts from the single laser light source 36 are
present equally in the light beams 26 and 28 conducted in the beam arms 32 and
34, since the light beams 26 and 28 are derived from the single input light
beam 38
(Fig. 1) which is transmitted through a single optical fiber 40. As a result,
any
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frequency and phase variations in the single input light beam 38 are canceled
by
common mode rejection when the light beams 26 and 28 are combined in the
single
output light beam 46. A similar common mode rejection occurs with respect to
phase differences introduced by movement or vibration of the optical fiber 48
which
conducts the output light beam 46 to the detector 50.
In addition to the beneficial aspects of the beam arms 32 and 34 allowing for
cancellation of the undesirable effects of disturbances by common mode
rejection,
the beam arms 32 and 34 also increase the number of fringes created.
Increasing
the number of fringes makes detecting and counting of the fringes easier to
accomplish, and increasing the number of fringes created also achieves a more
accurate measurement of the distance traveled by the freefall test mass 22.
The relationship of the number of fringes 60 relative to the change in the
light
beam path lengths caused by movement of the freefall test mass 22 relative to
the
stationary test mass 24 is known as an amplification factor. The gravimeter 20
produces an amplification factor of four, which is twice the amplification
factor from a
normal Michelson interferometer of the type used in most absolute gravimeters
such
as the one described in US patent 5,351,122. A Michelson interferometer
reflects
only one light beam from the freefall test mass. In this invention, both the
reflected
and reference the light beams 26 and 28 impinge upon and reflect from both of
the
test masses 22 and 24. As a result, the gravimeter 20 produces an interference
fringe signal that has a phase change equal to four times the difference in
the free-
fall distance of the test mass 22 relative to the reference test mass 24. This
relationship is shown in Fig. 6, where four interference fringes 60 in the
output light
beam 46 occur for each relative change in distance between the test masses 22
and
24 equal to one wavelength (A) of the input light beam 38 (Fig. 1). The
amplification
factor of four facilitates recognition of the fringes by the detector 50 and
the
controller/processor 52.
The amplification factor of four from the gravimeter 20 results from the
effect
of the gravity-induced acceleration on the test mass 22 during freefall
changing the
lengths of the beam arms 32 and 34. The relative change in the lengths of the
24
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beam arms 32 and 34 is four times the amount of relative physical separation
of the
test masses 22 and 24 during freefall. The following mathematical derivation
demonstrates the relationship of the four times change in relative length of
the beam
arms 32 and 34 compared to the physical separation distance of the test masses
22
and 24.
With the lower test mass 24 positioned stationarily and the upper test mass
22 freefalling the distance Zu, the beam arm 32 is shortened by the amount
2Zu,
because the beam arm segments 74c and 74d are each shortened by the amount
Zu, the distance that upper test mass 22 free falls. The beam arm segments
74a,
74b and 74e remain unchanged in length due to the stationary positions of the
lower
test mass 24 and the retroreflectors 70a and 70b. Simultaneously, the beam arm
34
is lengthened by a distance of 2Z,, because the downward movement of the
freefall
test mass 22 lengthens each of the beam arm segments 76d and 76e by the
amount Z. The beam arm segments 76a, 76b and 76c remain unchanged in length
due to the stationary positions of the lower test mass 24 and the
retroreflectors 70c
and 70d. Thus, the freefall of upper test mass 22 results in shortening the
overall
beam arm 32 by the distance 2Zu and lengthening the overall beam arm 34 by the
distance 2Zu.
When the upper test mass 22 falls freely, the optical path length of the beam
arm 32 will be changed by the difference in length of the beam arm 32. That
changed amount, referred to as ABA32is equal to -2Zu, with the negative value
indicating that the path length is shortened. Similarly, the optical path
length of the
beam arm 34 will be changed by the difference in length of the beam arm 34.
That
changed amount, referred to as ABA34 is equal to +2Zu, with the positive value
indicating that the path length is lengthened.
When light beams 26 and 28 from the two changed-length beam arms 32
and 34 are combined by the beam combiner 44, the combined output light beam 46
contains a sinusoidal interference fringe signal whose phase is given by the
difference in path length of the two beam arms 32 and 34. The difference in
optical
path length of the two beam arms 32 and 34, referred to herein as AL, is equal
to
CA 02896010 2015-06-30
the difference in change in length of the two beam arms 32 and 34, i.e. BA34
and
ABA32 , respectively. Stated mathematically, AL=ABA34-ABA32 , or AL=2Zu-(-2Z),
or
AL=4Zu. This mathematical derivation shows that the difference in path lengths
of
the beam arms 32 and 34 is equal to four times the distance that the upper
test
mass 22 falls relative to the lower stationary reference mass 24, thereby
mathematically demonstrating the amplification factor of four.
The amplification factor of four from the gravimeter 20 can also be
understood generally in terms of a differential frequency shift of the light
beams 26
and 28 in each of the beam arms 32 and 34 due to the well-known Doppler
effect.
The relative Doppler shift of light for a moving observer is given by the
equation f = fo
{(1 + v/c) / [(1 - (v/c)11/2), where fo is the frequency of light in the rest
frame of
reference and f is the frequency in the moving frame of reference, v is a
velocity of
the moving observer, and c is the speed of light. For velocities that are much
smaller than the speed of light, which is the case with respect to the
freefall test
mass 22, a first-order approximation is sufficient, so that f , fo (1 + v/c).
The change
in the frequency, Af = f - fo, therefore is proportional to the ratio of the
velocity of the
observer to the speed of light or Af = v/c fo.
The Doppler shift of a light beam reflecting from a moving mirror is twice
this
value or Af = 2 v/c fo. This can be understood because the moving mirror
"sees" a
Doppler shifted beam and then emits this new frequency upon reflection.
However
the new emitted Doppler shifted frequency is again Doppler shifted in the same
manner when observed by the stationary observer, which in the case of the
gravimeter 20, is any nonmoving portion of it. Each light beam 26 and 28
therefore
experiences a Doppler shift which is related to twice the velocity of the
freefall test
mass 22 from which the light beams 26 and 28 reflect.
The downward freefalling test mass 22 shifts the light beam 26 higher in
frequency when the light beam 26 reflects from the downward facing
retroreflector
72b and shifts the light beam 28 lower in frequency when the light beam 28
reflects
from the upward facing retroreflector 72a. The reflection of both light beams
26 and
28 in this manner has the net effect of giving an overall Doppler shift
proportional to
26
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twice the difference in velocity of the freefalling test mass 22 relative to
the
stationary test mass 24. The light beam 26 in the beam arm 32 is Doppler
shifted
positively to an increased frequency, while the light beam 28 in the other
beam arm
34 is Doppler shifted negatively to a decreased frequency. When the beams 26
and
28 are recombined, a signal with a frequency given by the difference of the
frequency of the light beam in each beam arm, or twice the Doppler shift in
the light
beam in one beam arm, is created. The resulting signal in the recombined
output
light beam is given by a Doppler shift proportional to four times the
differential
velocity of the two test masses 22 and 24. This factor of four is the same
factor of
four increase in signal arrived at using the above description of optical path
length
difference in the two beam arms.
The practical benefit of the improved resolution available from the
amplification factor of four is that the test mass 22 need only freefall a
reduced
distance to achieve adequate resolution for counting the fringes, compared to
a
greater freefall distance required with a lower amplification factor. A
gravimeter with
the higher amplification factor of four can be made smaller and more compact
than
a gravimeter having a lower amplification factor.
The previous discussion of functionality of the gravimeter 20 is that the
upper
test mass 22 freefalls while the lower test mass 24 is positioned stationarily
by the
long period isolation device 25. The situation could be reversed by allowing
the
lower test mass 24 to freefall while the upper test mass 22 is positioned
stationarily
by a long period isolation device 25. The same beneficial improvements result
from
this reversed situation, although the positive and negative values of the
changes in
optical path lengths of the beam arms 32 and 34 would be reversed in the
mathematical derivations described above.
Many other advantages and improvements will become apparent upon fully
appreciating the many aspects of the present invention. Presently preferred
embodiments of the present invention and many of its improvements have been
described with a degree of particularity. This description is preferred
examples of
implementing the invention, and is not necessarily intended to limit the scope
of the
27
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invention. The scope of the invention is defined by the scope of the following
claims.
28
