The invention is related to the technical field of interferometric free-fall gravity gradiometers.
Many gradiometers are known in the state of the art being able to measure the second derivative of the gravitational potential, i.e. the value of the gravity gradient.
Such a device is for instance disclosed in U.S. Pat. No. 3,693,451. This gravity gradiometer is based on dual free-falling objects in an evacuated vessel. For measurement of the second derivative of the gravitational potential a beam of laser light is generated which is split into two measuring beams. Each of both measuring beams is guided to one of the two free-falling objects. The measuring beams reflected by the objects are recombined and finally detected by a photo detector. Thus, the gradient of the gravitational force can be determined.
Recent science also utilizes atomic interferometry for determining the first or second derivative of the gravitational potential as e.g. disclosed in the publication “Measurement of gravitational acceleration by dropping atoms” of Peters et al., Nature, Vol. 400, pp. 849-852, Aug. 26, 1999. But like many other known systems, this system comprises at least one component which is fixed to the ground and is thus, albeit seismic isolation, sensitive to ground vibrations which inhibits very exact measurements. At least such a seismic isolation can be difficult or expensive to construct. This disadvantage generally occurs in many interferometric gradiometers.
U.S. Pat. No. 3,688,584 discloses another apparatus for measuring gravity gradients which is basically similar to the first mentioned device. In an embodiment of this apparatus two retroreflectors arranged above each other are caused to experience free flight. A laser is used to generate a beam of light which is guided to the system of two falling retroreflectors. The distance change between the two retroreflectors is determined by interfering reflected beams which are detected by a detector. The time rate of change of the frequency of the output signal of the detector is directly related to the vertical gradient of gravity, i.e. the second derivative of the gravitational potential.
However, there remains a need for a better characterization of the gravitational gradient. In particular knowledge of the third derivative of the gravitational potential, i.e. the derivative of the gravitational gradient is desired. Such information is of interest for many applications e.g. in aviation, space flight, for geological investigations or military applications since the knowledge of this third derivative could enhance the accuracy of many measurement devices.
Thus, the technical problem of the present invention is to obtain a system for determining changes of the gradient of the gravitation subject to height, and in particular for determining the third derivative of the gravitational potential.
The above mentioned technical problem is solved by the present invention comprising an interferometric free-fall gradiometer. This gradiometer comprises at least one source of coherent light and a first retroreflector which is able to fall freely in the gradiometer as well as a second retroreflector being able to fall freely in the gradiometer and disposed essentially under, preferably vertically under, the first retroreflector. Furthermore, the gradiometer comprises a light guiding assembly configured for guiding the coherent light to the first and second retroreflectors, thereby generating reflected beams and causing the reflected beams to interfere. In accordance with the present invention the gradiometer further comprises an assembly of a third and a fourth retroreflector able to fall freely in the gradiometer and disposed essentially between the first and second retroreflectors, whereas the at least one source of coherent light and the light guiding assembly are arranged for generating a first beam and a second beam of light, wherein the first beam is at least partially reflected by the first retroreflector and subsequently by the third retroreflector, or vice versa, and the second beam is at least partially reflected by the second retroreflector and subsequently by the fourth retroreflector, or vice versa, such that the interference of the resulting at least partially reflected first and second beams is indicative of the variation (change) of the distance between the first and the third retroreflectors and the distance between the second and the fourth retroreflectors.
With this gradiometer according to the invention, information about the third derivative of the gravitational potential can be obtained. This advantageous solution is not known by the prior art, since only one or two falling masses, respectively retroreflectors, are provided in the prior art. In detail, only the distance between two falling masses has been measured by prior art devices or even only the distance between one falling mass and a fixed second reflector or mirror resulting in the above mentioned disadvantages. Hence, no value or direct information with regard to the third derivative of the gravitational potential can be obtained with the prior art devices. Due to the distance measurements between the first and the third retroreflectors and the second and the fourth retroreflectors in accordance with the present invention, information about the third derivative of the gravitational potential is obtained.
In a preferred embodiment according to the invention all retroreflectors are arranged essentially in one vertical line. Such an arrangement of the four retroreflectors allows e.g. for an even better accuracy of the measurements with the gradiometer.
In a further embodiment of the gradiometer in accordance with the invention, the third retroreflector and the fourth retroreflector of the assembly of retroreflectors are connected to each other and are oppositely arranged. Although it is possible that the third and the fourth retroreflectors are not connected for measuring the paths, respectively the distances, between the first and the third retroreflectors and the second and the fourth retroreflectors, it is advantageous to provide the assembly of retroreflectors in such a form that the third and the fourth retroreflectors are connected, respectively coupled, to each other. In particular, in this configuration it is possible to construct the assembly of the third and the fourth retroreflectors in a manner that the optical centre of each of the third and fourth retroreflectors is located in the centre of mass of the retroreflector assembly. This arrangement helps in avoiding measurement errors which would be caused by different rotation of the single retroreflectors of the retroreflector assembly during free fall.
In yet another preferred embodiment of the present invention the coherent light has at least one linear polarization.
In yet another preferred embodiment the coherent light has at least two orthogonal linear polarizations and the guiding assembly further comprises a first non-polarizing beam splitter, arranged and adapted for splitting a beam of light generated by the source of light into the first beam and the second beam. Moreover, the guiding assembly comprises a first polarizing beam splitter arranged and adapted for splitting the first beam into a third beam and a fourth beam, wherein the first retroreflector is arranged and adapted for reflecting the third beam to the third retroreflector which is arranged and adapted for reflecting the third beam back to the first polarizing beam splitter, or vice versa, such that the third beam and the fourth beam can recombine in form of the first resulting beam. Furthermore, a second polarizing beam splitter is arranged and adapted for splitting the second beam into a fifth and a sixth beam, wherein the second retroreflector is arranged and adapted for reflecting the fifth beam to the fourth retroreflector which is arranged, and adapted for reflecting the fifth beam back to the second polarizing beam splitter, or vice versa, such that the fifth beam and the sixth beam can recombine in form of the second resulting beam. Additionally, a second non-polarizing beam splitter is provided for recombining the first resulting beam and the second resulting beam to a recombined beam; whereas the gradiometer further comprises a detector arranged for receiving the recombined beam. Hence, this embodiment renders an advanced device, respectively system, for measuring the third derivative of the gravitational potential. In particular, the distances between the first and the third retroreflectors and between the second and the fourth retroreflectors are determined, respectively measured. The information is carried by the resulting first and second beams. Preferably, these beams are brought to interference which is detected by the detector. Additionally, this gradiometer maintains the possibility of measuring the value of the second derivative of the gravitational potential because such information is provided in the resulting first beam or in the resulting second beam.
In yet another preferred embodiment of the gradiometer the first polarizing beam splitter is arranged essentially between the first retroreflector and the third retroreflector and the second polarizing beam splitter is arranged essentially between the second retroreflector and the fourth retroreflector whereas the gradiometer further comprises: a first lambda quarter plate being arranged between the first retroreflector and the first polarizing beam splitter, as well as a second lambda quarter plate being arranged between the third retroreflector and the first polarizing beam splitter. Additionally, the gradiometer preferably comprises a third lambda quarter plate being arranged between the second retroreflector and the second polarizing beam splitter, as well as a fourth lambda quarter plate being arranged between the fourth retroreflector and the second polarizing beam splitter. With the availability of such an advantageous gradiometer, the third derivative of the gravitational potential can also be determined. Furthermore, using the lambda quarter plates and the reflection in the corners of the corner cube reflectors enables a very compact design of the gradiometer.
In a further preferred embodiment of the gradiometer in accordance with the invention, the gradiometer further comprises a first polarization filter arranged in the path of the first resulting beam and/or a second polarization filter arranged in the path of second resulting beam.
In yet another preferred embodiment, the coherent light has at least two orthogonal linear polarizations and the light guiding assembly further comprises: a first non-polarizing beam splitter arranged and adapted for splitting a beam of light generated by the source of light into the first beam and the second beam, as well as a first polarizing beam splitter arranged and adapted for splitting the first beam into a third beam and a fourth beam, wherein the first retroreflector is arranged and adapted for reflecting the third beam to the third retroreflector which is arranged and adapted for reflecting the third beam back to the first polarizing beam splitter, or vice versa, such that the third beam and the fourth beam can recombine in form of the first resulting beam. Furthermore the light guiding assembly comprises a second polarizing beam splitter arranged and adapted for splitting the second beam into a fifth and a sixth beam, wherein the second retroreflector is arranged and adapted for reflecting the fifth beam to the fourth retroreflector which is arranged, and adapted for reflecting the fifth beam back to the second polarizing beam splitter, or vice versa, such that the fifth beam and the sixth beam can recombine in form of the second resulting beam. Moreover, in accordance with this embodiment the light guiding assembly further comprises a beam splitter assembly, wherein the beam splitter assembly is either arranged and adapted to at least partially recombine the first resulting beam and the second resulting beam to a recombined beam which can be received by a detector; or to reflect one of the resulting beams at least partially to a first detector and the second of the resulting beams at least partially to a second detector. Thus, this embodiment provides one preferable embodiment of a gradiometer which can be used for an easy determination of the third derivative of the gravitational potential as well as of the second derivative of the gravitational potential.
In accordance with a further preferred embodiment of the invention the coherent light source is adapted for providing light with at least one linear polarization and the guiding assembly further comprises: a first non-polarizing beam splitter arranged and adapted for splitting a beam of light generated by the source of light into the first beam and the second beam; and a first polarizing beam splitter or double mirror arranged and adapted for guiding the first beam to the first retroreflector, where it is reflected to the third retroreflector, or vice versa, and subsequently reflected by the first polarizing beam splitter or double mirror to form the first resulting beam. Moreover, preferably a second polarizing beam splitter or double mirror is arranged and adapted for guiding the second beam to the second retroreflector, wherein the latter is reflected to the fourth retroreflector, or vice versa, and is subsequently reflected by the second polarizing beam splitter or double mirror to form the second resulting beam. Finally, a second non-polarizing beam splitter is preferably comprised for recombining the first resulting beam and the second resulting beam to a recombined beam. At last, the gradiometer further preferably comprises a detector arranged for receiving the recombined beam. One advantage of this preferred embodiment is the relatively simple design which can also be used to obtain information about the third derivative of the gravitational potential.
In accordance with yet a further preferred embodiment of the invention the generated coherent light has at least two orthogonal polarizations, whereas the guiding assembly comprises: a first polarizing beam splitter or double mirror arranged and adapted for guiding the first beam to the first retroreflector where it is reflected to the third retroreflector, or vice versa, and subsequently reflected by the first polarizing beam splitter or double mirror to form the first resulting beam. Additionally, the second polarizing beam splitter or double mirror is arranged and adapted for guiding the second beam to the second retroreflector where it is reflected to the fourth retroreflector, or vice versa, and subsequently reflected by the second polarizing beam splitter or double mirror to form the second resulting beam. Furthermore, the guiding assembly further comprises an initial polarizing beam splitter arranged and adapted for splitting the beam of light generated by the source of light into the first beam and the second beam, whereas the first beam exhibits a first polarization and the second beam exhibits a second polarization. At last, a recombining beam splitter is arranged and adapted for recombining the first resulting beam and the second resulting beam to a recombined beam, whereas the gradiometer further comprises a detector which is arranged for receiving the recombined beam. This preferred embodiment provides another effective way of providing a gradiometer for determining the third derivative of the gravitation potential.
Moreover, in accordance with this preferred embodiment a polarizer may be arranged in the path of the recombined beam between the recombining beam splitter and the detector for receiving an improved detectable signal.
In yet another embodiment of the gradiometer according to the invention the first polarizing beam splitter or double mirror is preferably arranged essentially between the first retroreflector and the third retroreflector and/or the second polarizing beam splitter or double mirror is preferably arranged essentially between the second retroreflector and the fourth retroreflector.
In another preferred embodiment of the invention each of the reflectors is a corner cube retroreflector which can be either arranged such that a respective incident beam of light is reflected with a lateral offset or can be arranged such that the incident beam of light is reflected by the corner of the corner cube retroreflector. Hence, depending on the desired arrangement a beam of light may be reflected with a lateral offset or be reflected by 180 degrees in essentially one point.
In accordance with yet another preferred embodiment of the invention the distance between the first retroreflector and the third retroreflector is equal to the distance between the second retroreflector and the fourth retroreflector. Other distances could be chosen but especially this arrangement is in particular convenient for determining the third derivative of the gravitational potential.
In accordance with yet another preferred embodiment of the invention each of the third and the fourth retroreflectors of the retroreflector assembly is arranged and adapted to receiving (incident) beams of light essentially in parallel to the vertical direction and reflecting the (incident) beams of light essentially in parallel to the vertical direction. In particular, the assembly of retroreflectors may comprise two corner cube reflectors being directed in opposite directions and being connected with each other. Thus, each one of both corner cube reflectors of the retroreflector assembly is adapted to receive and reflect beams of light essentially in parallel to the vertical direction.
In the following reference is made to the Figures of the preferred embodiments of the invention. More details can be found in the detailed description of the preferred embodiments of the invention.
In general, the retroreflector assembly TM2 preferably contains two retroreflectors, rigidly connected to each other. The upper retroreflector shows upward, the lower one downward. However, it is also possible to provide a retroreflector assembly with two distinct retroreflectors either arranged in one vertical line or arranged essentially side by side. Preferably, the second retroreflector TM3 is arranged vertically below the first retroreflector TM1 with the retroreflectors of retroreflector assembly TM2 between them.
One aim of the gradiometer is basically to conduct a double differential measurement. The first beam can measure the path length change between retroreflector TM1 and the respective retroreflector of retroreflector assembly TM2, i.e. the upper retroreflector of the retroreflector assembly. The second beam can measure the path length change between retroreflector TM3 and the second retroreflector of the retroreflector assembly TM2, i.e. the lower retroreflector of the retroreflector assembly TM2. Of course it has to be appreciated that the wordings upper and lower must not be understood as limiting and shall only describe the position of the reflectors in accordance with
As already mentioned above, one important application of the gradiometer in accordance with the invention is for example the measurement of non-linearity in the gravity gradient (third derivative of the gravitational potential). If it is assumed that retroreflectors TM1, TM3, and the retroreflectors of retroreflector assembly TM2 are aligned along the plumb line as shown in
However, if it is assumed that the magnitude of the gravity gradient between retroreflectors TM1 and retroreflector assembly TM2 is different from its magnitude between retroreflector assembly TM2 and retroreflector TM3, which is in general the case, the path length change in the first resulting beam will be different from the second resulting beam. The result is a signal, which gives information about the deviation from linearity of the gravity.
Thus, the first beam and the second beam can be considered as two independent gravity gradiometers, which can measure the absolute value of the gravity gradient, mainly its constant part. In the first resulting beam and in the second resulting beam information is included which could be used to obtain the value of the gravity gradient, e.g. by placing a detector in the path of the first resulting beam or the second resulting beam for detection of an interference pattern.
A second possible application of the gradiometer in accordance with the invention is the measurement of the gravity field of a well defined source mass. Thus, it is obtained a method for determining, respectively measuring, the gravitational constant G. As also depicted in
Furthermore, it is remarked that any source masses (SM1, SM2) are not necessarily part of the present gradiometer. They are just shown as a possible application, namely for the measurement of the gravitational constant, G. However, the source masses SM1, SM2 may also be part of the gradiometer.
A second embodiment of a gradiometer in accordance with the present invention is depicted in
Afterwards, the second mode is reflected back to polarizing beam splitter PBS1. During this path the beam crosses twice a lambda quarter plate λ/4 which rotates the polarization by 90°. This allows the beam now to pass the polarizing beam splitter PBS1 without deflection to hit retroreflector assembly TM2. During this path its polarization is turned again by 90° by crossing twice a lambda quarter plate λ/4. The beam is deflected now at polarizing beam splitter PBS1 to superpose with the first beam. Afterwards the two polarization modes are made equal at polarizer Pol1. The beam then passes non-polarizing beam splitter BS2 and hits the photo detector D. By just observing this signal the upper beam works as a first gradiometer, with which the gravity difference between retroreflector TM1 and the upper retroreflector of retroreflector assembly TM2 can be measured. The path of the lower beam is similar to the upper path, with the difference that now the beam hits the lower retroreflector of retroreflector assembly TM2 and retroreflector TM3. Polarizer Pol2 is preferably adjusted in a manner to coincide the two polarization modes in the lower beam and, in addition, preferably to coincide it with the upper beam. Non-polarizing beam splitter BS2 superposes upper beam and lower beam. The resultant signal received by the detector D contains the information about the gravity difference between retroreflector TM1 and the upper retroreflector of TM2, and the lower retroreflector of TM2 and retroreflector TM3. That means a double differential measurement is at hand.
As in
In general, it is remarked that mirrors M1, M2, polarizers Pol1, Pol2, Pol3, Pol4, Pol and polarizing beam splitters PBS1, PBS2, PBS3, PBS can be easily arranged and adapted operatively by the person skilled in the art of interferometric gradiometers. As in the above embodiment the non-polarizing beam splitters BS1 and BS2 are preferably intensity beam splitters, e.g. 50/50 beam splitters. Furthermore, the mirrors, polarizers and beam splitters may be adjusted by the person skilled in the field of interferometric gradiometers to achieve an operative, respectively functional, setup.
Additionally, it is remarked that the interpretation of interference patterns obtained by interferometric free fall gradiometry is in general also known by the skilled person. This applies as well to the known phenomenon of the Doppler-Shift which occurs in general in measurements using interferometric free fall gradiometers due to changing distances between reflectors, respectively their relative movement.
In general, the construction of a common free-fall gradiometer is known comprising e.g. elevators for lifting test masses, respectively the retroreflectors and devices for breaking their free fall. Such devices are not in the scope of the present invention and can be constructed in accordance with the technical knowledge of the skilled person.
Furthermore, the first and the second coherent beams of light could also be generated by two different sources of light. However, it is preferred that all utilized light beams are generated by the same source of coherent light.
At last, it is mentioned that the features of each the above described embodiments can be combined with each other. Moreover, constructive details can be adapted or changed by the skilled person in view of the desired design.
BS non-polarizing beam splitter
BS1 non-polarizing beam splitter
BS2 non-polarizing beam splitter
D detector
D1 detector 1
D2 detector 2
DM1 first double mirror
DM2 second double mirror
d distance
d/2 half distance of distance d
g gravity acceleration
M1 mirror
M2 mirror
L light source
PBS polarizing beam splitter
PBS1 first polarizing beam splitter
PBS2 second polarizing beam splitter
PBS3 third polarizing beam splitter
Pol polarizer
Pol1 polarizer
Pol2 polarizer
Pol3 polarizer
Pol4 polarizer
SM1 source mass
SM2 source mass
TM1 retroreflector/test mass
TM2 retroreflector/test mass
TM3 retroreflector assembly/test mass assembly
λ/2 lambda half plate
λ/4 lambda quarter plate
Number | Date | Country | Kind |
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10150827.3 | Jan 2010 | EP | regional |
Filing Document | Filing Date | Country | Kind | 371c Date |
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PCT/EP2011/050102 | 1/5/2011 | WO | 00 | 11/28/2012 |