# US 2014/0190255 A1 · Ultra high resolution gravity gradiometery technique

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- Number: US 2014/0190255 A1
- Document ID: US20140190255A1
- Status: Published application
- Kind: A1
- Application number: 13/725,849
- Filed: 2012-12-21
- Published: 2014-07-10
- Earliest claimed: 2011-12-22
- Assignees: California Institute of Technology
- Inventors: Shervin Taghavi Larigani
- Web page: https://patentgrep.com/patent/US20140190255A1

## CPC

- G01V 7/04: Electric, photoelectric, or magnetic indicating or recording means
- G01S 11/12: using electromagnetic waves other than radio waves
- G01V: GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS (means for indicating the location of accidentally buried, e.g. snow-buried, persons A63B29/02)
- G01S: RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES

## Abstract

A method and system provide the ability to measure relative displacement and rotation. A first light is continuously shined from a first light source that is fixed on a first entity to a first two-dimensional (2D) plate fixed on a second entity. The first direction of propagation of the first light does not change relative to the first entity. A second light is shined from a second light source that is fixed on the first entity to a second 2D plate fixed on the second entity. A second direction of propagation of the second light does not change relative to the first entity and is different from the first direction of propagation. The displacement of the lights on plates is directly monitored to determine a 3D displacement vector that represents a relative displacement between the first entity and the second entity. Thus, a three dimensional gravity gradient tensor is constructed.

## Claims

### Claim 1

A method for measuring a relative displacement and rotation, comprising:
continuously shining a first light from a first light source that is fixed on a first entity to a first two-dimensional (2D) plate fixed on a second entity, wherein a first direction of propagation of the first light does not change relative to the first entity;
continuously shining a second light from a second light source that is fixed on the first entity to a second 2D plate fixed on the second entity, wherein a second direction of propagation of the second light does not change relative to the first entity, and wherein the first direction of propagation is different from the second direction of propagation; and
monitoring displacement of the first light on the first plate and the second light on the second plate to directly determine a three-dimensional (3D) displacement vector that represents a relative displacement in three dimensions between the first entity and the second entity.

### Claim 2 (depends on 1)

The method of claim 1, wherein the first entity and the second entity are both satellites.

### Claim 3 (depends on 1)

The method of claim 1, further comprising:
continuously shining a third light from a third light source that is fixed on the second entity to a third 2D plate fixed on the first entity, wherein a third direction of propagation of the third light does not change relative to the second entity;
continuously shining a fourth light from a fourth light source that is fixed on the second entity to a fourth 2D plate fixed on the first entity, wherein a fourth direction of propagation of the fourth light does not change relative to the second entity, and wherein the third direction of propagation is different from the fourth direction of propagation;
monitoring displacement of the third light on the third plate and the fourth light on the fourth plate; and
determining which entity causes the relative displacement based on the displacement monitoring from the first light, second light, third light, and fourth light.

### Claim 4 (depends on 3)

The method of claim 3, wherein:
the determining is based on a delay associated with a duration taken for third light and the fourth light to travel from the second entity to the first entity; and
the displacement monitoring is conducted faster than a time it takes for the third light and the second light to travel from the second entity to the first entity.

### Claim 5 (depends on 3)

The method of claim 3, wherein:
a rate of collecting data for the displacement vector is determined by a photon counting regime, wherein the photon counting regime comprises a time separating two consecutive photons hitting a detector; and
as long as a photons arriving at the third plate do not reach the photon counting regime, data is collected.

### Claim 6 (depends on 1)

The method of claim 1, wherein:
relative displacement as small as
W

(
z
)
SS
is measured, where W is the width of the first light in a z-direction after being reduced to its optical limit of
λ
π
and SS=G·Nphoton is a signal-size being detected at a detection where G comprises a gain of an optical detector and Nphoton is a number of photons.

### Claim 7 (depends on 1)

The method of claim 1, further comprising:
utilizing the 3D displacement vector to quantify a gravity potential of a third entity.

### Claim 8 (depends on 7)

The method of claim 7, further comprising:
utilizing the gravity potential to spatially and temporally measure physical parameters of the third entity that is inducing change in the gravity potential.

### Claim 9 (depends on 1)

The method of claim 1, wherein the 3D displacement vector comprises a relative rotation between the first entity and the second entity.

### Claim 10

An system for measuring a relative displacement and rotation comprising:
(a) a first light source, wherein:
(i) the first light source is fixed on a first entity;
(ii) the first light source continuously shines a first light to a first two-dimensional (2D) plate fixed on a second entity; and
(iii) a first direction of propagation of the first light does not change relative to the first entity;
(b) a second light source, wherein:
(i) the second light source is fixed on the first entity;
(ii) the second light source continuously shines a second light to a second 2D plate fixed on the second entity;
(iii) a second direction of propagation of the second light does not change relative to the first entity; and
(iv) the first direction of propagation is different from the second direction of propagation; and
(c) the second entity is configured to directly monitor displacement of the first light on the first plate and the second light on the second plate to determine a three-dimensional (3D) displacement vector that represents a relative displacement in three dimensions between the first entity and the second entity.

### Claim 11 (depends on 10)

The system of claim 10, wherein the first entity and the second entity are both satellites.

### Claim 12 (depends on 10)

The system of claim 10, further comprising:
(d) a third light source, wherein:
(i) the third light source is fixed on the second entity;
(ii) the third light source continuously shines a third light to a third 2D plate fixed on the first entity; and
(iii) a third direction of propagation of the third light does not change relative to the second entity;
(e) a fourth light source, wherein:
(i) the fourth light source is fixed on the second entity;
(ii) the fourth light source continuously shines a fourth light to a fourth 2D plate fixed on the first entity;
(iii) a fourth direction of propagation of the fourth light does not change relative to the second entity; and
(iv) the third direction of propagation is different from the fourth direction of propagation;
(f) the first entity is configured to monitor displacement of the third light on the third plate and the fourth light on the fourth plate; and
wherein: a determination regarding which entity causes the relative displacement is based on the displacement monitoring from the first light, second light, third light, and fourth light.

### Claim 13 (depends on 12)

The system of claim 12, wherein:
the determination is based on a delay associated with a duration taken for third light and the fourth light to travel from the second entity to the first entity; and
the displacement monitoring is conducted faster than a time it takes for the third light and the second light to travel from the second entity to the first entity.

### Claim 14 (depends on 12)

The system of claim 12, wherein:
a rate of collecting data for the displacement vector is determined by a photon counting regime; and
as long as a photons arriving at the third plate do not reach the photon counting regime, data is collected.

### Claim 15 (depends on 10)

The system of claim 10, wherein:
relative displacement as small as
W

(
z
)
SS
is measured, where W is the width of the first light in a z-direction after being reduced to its optical limit of
λ
π
,
and SS=G·Nphoton is a signal-size being detected at a detection where G is the gain of the optical detector and Nphoton is the number of photons.

### Claim 16 (depends on 10)

The system of claim 10, further comprising:
a quantifying entity that is configured to utilize the 3D displacement vector to quantify a gravity potential of a third entity.

### Claim 17 (depends on 16)

The system of claim 16, wherein:
the gravity potential is utilized to spatially and temporally measure physical parameters of the third entity that is inducing a change in the gravity potential.

### Claim 18 (depends on 10)

The system of claim 10, wherein the 3D displacement vector comprises a relative rotation between the first entity and the second entity.