Abstract:
The invention relates to a gravity measurement apparatus comprising a torsion balance bearing a test mass. The torsion balance has a predetermined center of mass and is rotatable around a predetermined rotation axis, wherein the torsion balance is asymmetric in such a way that the center of mass of the torsion balance is offset to the rotation axis of the torsion balance.

Description:
FIELD OF THE INVENTION  
       [0001]     The invention relates to a gravity measurement apparatus, and more particularly to apparatus suitable for precision surveillance of the gravitational field of the earth, mapping of local changes in gravitational gradients (e.g. for the search for mineral deposits) or mapping of variations in tidal forces (in climate and geographic research).  
       BACKGROUND  
       [0002]     For a long time, it is well known in the state of the art to use torsion balances to measure gravity forces. These torsion balances are disclosed, for example, in Dorobantu, R.: “Gravitionsdrehwaage,” IAPG/FESG No. 4, 1999. They comprise a horizontal balance beam, which is suspended from a torsion wire defining a rotation axis. The balance beam bears two test masses on opposite sides of the torsion wire so that the torsion balance is symmetric and the center of mass of the torsion balance is in line with the rotation axis of the torsion balance. Therefore, these conventional symmetric torsion balances compensate for the gravitational attraction g of the earth, so that differential forces can be determined using the so-called “Null measurements” (e.g. tests of the “equivalence principle” as disclosed in SMITH et al.: “Short-range tests of the equivalence principle,” Physical Review D, Volume 61, 022001, 1999). The advantage of these conventional symmetric torsion balances is their very high precision with relative accuracies down to 10 −13  (cf. SMITH et al.). However, the conventional symmetric torsion balances merely allow the measurement of differential forces, whereas the measurement of absolute values of gravity forces is not possible.  
         [0003]     Further, symmetric torsion balances with more complex mass distributions (quadrupole or octupole) are known from V.B. BRAGINSKY, V.I. PANOV: “Verification of the equivalence of inertial and gravitational mass”, JETP 34, 463 (1972). These torsion balances are commonly used for eliminating certain orders of gravitational fields.  
         [0004]     Therefore, it is an object of the invention to provide a gravity measurement apparatus allowing the measurement of absolute values of gravity forces.  
         [0005]     Further, it is an object of the invention to combine the high precision of the aforementioned symmetric torsion balances with the possibility to measure absolute values of gravity forces.  
       SUMMARY  
       [0006]     These and other objects are achieved by a gravity measurement apparatus comprising a torsion balance bearing a test mass, said torsion balance having a predetermined center of mass and being rotatable around a predetermined rotation axis, wherein the torsion balance is asymmetric in such a way that the center of mass of the torsion balance is shifted relative to the rotation axis of the torsion balance. In other words, the torsion balance does not have a symmetric mass distribution as the aforementioned symmetric torsion balances according to the state of the art. Instead, the torsion balance according to the invention comprises a torsion balance having an asymmetric mass distribution with regard to the rotation axis, so that absolute value measurements of gravity forces are possible. Therefore, the torsion balance of the invention preferably comprises a single test mass only.  
         [0007]     The gravity measurement apparatus according to the invention is particularly suitable for the measurement of varying gravity forces with long periods such as gravitational interaction between the gravity measurement apparatus and cosmic objects (e.g. the sun). However, the gravity measurement apparatus according to the invention can be used in a variety of tasks, e.g. precision surveillance of the gravitational field of the earth, mapping of local changes in gravitational gradients (e.g. in the search for mineral deposits) or mapping of variations in tidal forces (e.g. in climate and geographic research).  
         [0008]     Unlike the aforementioned well-known symmetric torsion balances, the inventive asymmetric torsion balances does not inherently compensate for the gravitational attraction g of the earth. Instead, the gravitational attraction g of the earth is preferably compensated by an electrostatic feedback device for applying an electrostatic feedback force to the torsion balance.  
         [0009]     The electrostatic feedback device preferably comprises at least a first feedback electrode attached to the torsion balance for applying the electrostatic feedback force to the torsion balance. With regard to the rotation axis of the torsion balance the first feedback electrode is preferably arranged opposite the test mass so that the electrostatic feedback force causes a torque acting on the torsion balance for compensating the gravitational attraction g of the earth.  
         [0010]     The axis of the torque generated by the first feedback electrode is preferably aligned perpendicular to the rotation axis of the torsion balance and also perpendicular to the longitudinal axis of the torsion balance. Therefore, the torque generated by the first feedback electrode compensates the asymmetric mass distribution of the torsion balance so that the torsion balance is kept horizontal.  
         [0011]     Further, the first feedback electrode is preferably flat and aligned perpendicular to the rotation axis of the torsion balance so that the electrostatic feedback force acting on the first feedback electrode is aligned parallel to the rotation axis of the torsion balance.  
         [0012]     In the preferred embodiment of the invention the electrostatic feedback device comprises a set of second feedback electrodes attached to the torsion balance, said second feedback electrodes being flat and aligned perpendicular to each other and parallel to the rotation axis of the torsion balance. Therefore, the second feedback electrodes can be used to apply a rotational feedback torque on the torsion balance with regard to the rotation axis of the torsion balance.  
         [0013]     Further, the second feedback electrodes can be used for damping movements of the torsion balance. Particularly, common swinging pendulum modes and rotational oscillatory modes can be damped by the second feedback electrodes.  
         [0014]     Further, the first and second feedback electrodes are preferably driven by capacitors into which the first and second feedback electrodes extend so that the electrical field within the capacitors acts on the first and second feedback electrodes causing the electrostatic feedback forces. Therefore, the capacitors are preferably aligned parallel to the first and second feedback electrodes.  
         [0015]     The aforementioned feedback mechanism of applying a feedback voltage to a feedback capacitor is illustrated in Z. ZHOU, J. LUO: “On the significance of electrical damping in torsion balance”, Chinese Physics Letters Vol. 14, No. 8 (1997) 565, so that this publication is incorporated herein by reference.  
         [0016]     In the preferred embodiment the first and second feedback electrodes at least partially consist of glass plates, which can be covered with an electrically conducting material (e.g. metals such as gold).  
         [0017]     Further, it should be noted that the invention is not restricted to a gravity measurement apparatus comprising an electrostatic feedback device. Instead of the electrostatic feedback device a magnetic feedback device or any other type of force feedback devices can be used for compensating for the gravitational attraction g of the earth and for damping oscillatory movements of the torsion balance.  
         [0018]     In the preferred embodiment of the invention, the torsion balance is arranged within a Faraday cage shielding the torsion balance at least partially from electrostatic disturbances. The Faraday cage can be realized by a box consisting of an electrically conductive material (e.g. aluminium).  
         [0019]     Further, the gravity measurement apparatus according to the invention preferably comprises a magnetic cage shielding the torsion balance at least partially from magnetic disturbances. The magnetic cage can be realized by encasing the torsion balance by so-called μ-metal foil with a high magnetic permeability.  
         [0020]     In the preferred embodiment the gravity measurement apparatus according to the invention further comprises a thermal insulation shielding the torsion balance at least partially from thermal disturbances.  
         [0021]     Moreover, the gravity measurement apparatus preferably comprises a vacuum chamber encasing the torsion balance, so that thermal gradients and residual air pressure in the vicinity of the torsion balance are further reduced.  
         [0022]     Further, the gravity measurement apparatus according to the invention preferably comprises an optical readout device for detecting the position of the torsion balance, particularly the angular position of the torsion balance.  
         [0023]     The optical readout device preferably comprises a first mirror and a second mirror, said first mirror and said second mirror being attached to the torsion balance and being aligned perpendicular to each other and parallel to the rotation axis.  
         [0024]     Further, the optical readout device preferably further comprises a first light source directing a first light beam onto the first mirror, a first light detector detecting the first light beam after its reflection by the first mirror, a second light source directing a second light beam onto the second mirror and a second light detector detecting the second light beam after its reflection by the second mirror. Therefore, the first and second light beams are being reflected by the first and second mirrors attached to the torsion balance. These light beams are preferably aligned perpendicular to each other.  
         [0025]     The first and second light detectors are preferably four quadrant photo detectors (e.g. four quadrant photo diodes), so that movements of the suspended torsion balance can be tracked in any allowed translational or rotational degree of freedom.  
         [0026]     Further, the optical readout device preferably applies the so-called “lock-in technique” for improving the signal-to-noise ratio of the measurement. Therefore, the optical readout device preferably comprises a lock-in amplifier receiving as one input an electrical measurement signal from the light detectors and as a second input a frequency reference, which is also used to modulate the light beams by a modulator, e.g. by means of AOM (Acousto-optical modulation). Therefore, the modulator is preferably an acousto-optical modulator. However, it is also possible to use an EOM (Electro-optical modulator) or other types of optical modulators.  
         [0027]     Sending the electrical measurement signal generated by the light detectors to the same lock-in amplifier as the frequency reference used for modulation of the light beams generates a DC (direct current) signal out of exactly one frequency component of the detected electrical measurement signal. Now one assumes that the electrical measurement signal contains a lot of disturbing influences with a variety of different frequency components. Therefore, the optical readout device preferably comprises a bandpass filter filtering the electrical measurement signal before its amplification by the lock-in amplifier.  
         [0028]     The bandpass filter preferably comprises a centre frequency corresponding to the frequency reference used for modulation of the light beams which supports the aforementioned lock-in technique.  
         [0029]     The aforementioned optical readout device is also disclosed in PAUL LORRAIN: “An optical lever for measuring very small rotational oscillations”, Optics and Lasers in Engineering 15 (1991), 197-201. Therefore, the content of this publication is incorporated by reference herein.  
         [0030]     The torsion balance is preferably suspended from a torsion wire or a torsion strip as a supporting torsion member as in conventional symmetric torsion balances. The torsion wire or the torsion strip preferably consists of tungsten, silver, copper, platinum or iridium. However, the torsion wire may also consist of quartz fibers with a metal coating. Further, the torsion wire preferably has a diameter between 5 μm and 50 μm. In principle, larger diameters of the torsion wire are possible. However, this would decrease the sensitivity of the torsional motion. The diameter of the torsion balance can be tuned in a wide range for many applications. In some cases it might even be useful to decrease the sensitivity deliberately in order to reduce certain noise components.  
         [0031]     The torsion strip for suspension of the torsion balance is disclosed, for example, in RICHMAN et al.: “Preliminary determination of G using the BIPM torsion strip balance”, Meas. Sci. Technol. 10 (1999) 460-466. Therefore, this publication is incorporated by reference herein.  
         [0032]     The torsion wire or the torsion strip preferably consist of an electrically conductive material so that the torsion balance can be electrically grounded by the torsion wire or the torsion strip.  
         [0033]     It may be desirable to include in combination with an electrostatic feedback device a magnetostatic feedback for compensation of vertical movements of the torsion balance along the rotation axis.  
         [0034]     Further, the torsion balance preferably comprises a main structure (e.g. a rod) being aligned coaxially with the rotation axis and being suspended from the wire. In a preferred embodiment of the invention the main structure is constructed from a solid vertical aluminium body having a quadratic cross section. Further, the torsion balance may comprise a horizontal secondary structure (e.g. a stick or beam) bearing the test mass on one end and the first feedback electrode on the opposite end, wherein said secondary structure is attached to the main structure and being aligned perpendicular to the rotation axis of the torsion balance.  
         [0035]     The torsion balance is preferably electrically grounded to avoid any electrostatic disturbances, e.g. by the torsion wire itself. Therefore, the torsion balance preferably consists of an electrically conductive material (e.g. aluminium). Alternatively, the torsion balance might be coated with an electrically conductive coating. In the latter case the torsion balance might even consist of an electrically insulating material. For example, the torsion balance might consist of glass having a golden coating.  
         [0036]     Further, the torsion balance preferably consists of a non-magnetic material (e.g. aluminium) to avoid any magnetic disturbance.  
         [0037]     Other features and advantages of the invention will become apparent from the following description of a preferred exemplary embodiment considered with the accompanying drawings.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0038]      FIG. 1A  shows a perspective view of a torsion balance according to the invention;  
         [0039]      FIG. 1B  shows a side view of the torsion balance according to  FIG. 1A ;  
         [0040]      FIG. 2  is a perspective view showing the torsion balance suspended from a torsion wire;  
         [0041]      FIG. 3  is a perspective view of the torsion balance and an electrostatic feedback device for compensating the gravitational attraction of the earth and for damping oscillatory movements of the torsion balance;  
         [0042]      FIG. 4  is a perspective view showing the torsion balance, the electrostatic feedback device and an optical readout device for detecting the position of the torsion balance;  
         [0043]      FIG. 5  is a top view of the gravity measurement apparatus showing the optical readout device and the electrostatic feedback device;  
         [0044]      FIG. 6  is a perspective view showing a box shielding the torsion balance from electrostatic, magnetic and thermal disturbance;  
         [0045]      FIG. 7  is a perspective view showing a vacuum chamber containing the torsion balance; and  
         [0046]      FIG. 8  is a schematic of the optical readout device of the gravimeter shown in  FIGS. 1-7 . 
     
    
     DETAILED DESCRIPTION  
       [0047]      FIGS. 1A and 1B  illustrate an asymmetric torsion balance  1  comprising a vertical alninium rod  2  which is suspended from a torsion wire  3  at its top  4 . The torsion wire  3  has a diameter of 25 μm and consists of tungsten. Further, the torsion wire  3  defines a rotation axis  5  of the torsion balance  1 , so that the torsion balance  1  can rotate around the rotation axis  5 .  
         [0048]     Further, a horizontal beam  6  is fixed along the middle of the vertical rod  2 . On one side of the beam  6  a single test mass  7  is attached, and on the other side of the beam  6  a first feedback electrode  8  is attached for applying an electrostatic feedback force to the torsion balance  1 , which will be described later.  
         [0049]     At the bottom of the vertical rod  2  a set of second electrodes  9  is attached, which are aligned perpendicular to each other and parallel to the rotation axis  5  of the torsion balance  1 . Therefore, the second feedback electrodes  9  can be used to apply a rotational feedback torque on the torsion balance  1  with regard to the rotation axis  5 . Further, the second feedback electrodes  9  can be used for damping movements of the torsion balance  1 . Particularly, common swinging pendulum modes and rotational oscillatory modes can be damped by the second feedback electrodes  9 .  
         [0050]     Further, a first mirror  10  and a second mirror  11  (see  FIG. 1A ) are attached to the side surfaces of the vertical rod  2  near the top  4 . The first and second mirrors  10 ,  11  are part of an optical readout device, which is used to determine the angular position of the torsion balance  1  and which will be described later.  
         [0051]     It is an essential feature of the torsion balance  1  that it comprises an asymmetric mass distribution so that it allows the measurement of absolute values of gravity forces. Therefore,  10  the torsion balance  1  comprises a center of mass  12  (see  FIG. 1B ), which is shifted horizontally with regard to the rotation axis  5  of the torsion balance  1 .  
         [0052]     Referring to the coordinate system illustrated in  FIG. 1A  there are the following degrees of freedom for the torsion balance  1 :  
         [0053]     Translatory movements along x-axis and y-axis;  
         [0054]     Rotary movements around x-axis and z-axis (rotation axis  5 ).  
         [0055]     However, rotational motions around the y-axis are suppressed due to the geometrical symmetry of the torsion balance  1  in this degree of freedom. Further, translational movements along the z-axis are forbidden due to the suspension of the torsion balance  1  and the attraction of the torsion balance  1  by the gravitational attraction of the earth.  
         [0056]      FIG. 2  illustrates the suspension of the torsion balance  1  in the gravity measurement apparatus according to the invention. Therefore, the gravity measurement apparatus according to the invention comprises a base  13  supporting a vertical column  14 . At the top of the column  14  there is a horizontal arm  15  to which the torsion wire  3  is attached. The arm  15  can be moved freely to position the torsion balance  1  precisely.  
         [0057]      FIG. 3  illustrates the aforementioned electrostatic feedback device, which will be explained in the following.  
         [0058]     The electrostatic feedback device comprises a first capacitor  16  having flat and horizontally aligned parallel capacitor plates  16 A and  16 B, wherein the first capacitor  16  is encapsulated by a housing consisting of an upper part  17  and a lower part  18 . The capacitor  16  applies an electrostatic feedback force to the first feedback electrode  8  of the torsion balance  1  along the z-axis. The electrostatic feedback force caused by the capacitor  16  is used for compensating the gravitational attraction g of the earth.  
         [0059]     Further, the electrostatic feedback device comprises a set of second capacitors  19 ,  20 ,  21  and  22 , which are mounted on a base plate  23 . The second capacitors  19 - 22  are aligned parallel to the rotation axis  5  defined by the torsion wire  3  and perpendicular to each other. Therefore, the second capacitors  19 - 22  apply a torque to the torsion balance  1  with regard to its rotation axis  5 . The torque caused by the second capacitors  19 - 22  can be used for damping oscillatory rotary motions of the torsion balance  1  with regard to its rotation axis  5  and pendulum swinging modes. Further, the second capacitors  19 - 22  can be used to apply a rotational feedback to the torsional balance  1  after the initial oscillatory rotational movements of the torsion balance  1  have disappeared due to the afore-mentioned damping.  
         [0060]     The first capacitor  16  and the second capacitors  19 - 22  can be driven independently from each other with different voltages by a computer control which is based on PID (Proportional-Integral-Differential) controllers for each input channel. The feedback signal consists of a constant (offset) part and additional small voltage outputs fed to the first capacitor  16  and the second capacitors  19 - 22 . Therefore, motions in all degrees of freedom can thus be compensated for.  
         [0061]      FIGS. 4 and 5  illustrate an optical readout device for detecting the angular position of the torsion balance  1  with regard to the degrees of freedom mentioned above.  
         [0062]     The optical readout device comprises a first optical module  24  and a second optical module  25 , which have an identical design, so that in the following the optical module  25  is illustrated only.  
         [0063]     The second optical module  25  of the optical readout device comprises a fiber outcoupler  26  connected to an optical fiber  27  through which an optical signal is fed to the fiber outcoupler  26 .  
         [0064]     Further, the second optical module comprises a beamsplitter cube  28 , a mirror  29  and a four quadrant photo diode detector  30 .  
         [0065]     The fiber outcoupler  26 , the beamsplitter cube  28 , the mirror  29  and the detector  30  are mounted on a base plate  31 , as can be seen in  FIG. 4 .  
         [0066]     The fiber outcoupler  26  couples a light beam out of the optical fiber  27  and the beamsplitter cube  28  directs a light beam  32  onto the second mirror  11  ( FIG. 1A ) of the torsion balance  1 . The light beam  32  is reflected by the second mirror  11  of the torsion balance  1  and the mirror  29  of the second optical module  25  of the optical readout device so that finally the detector  30  detects the reflected light beam  32 . Therefore, movements of the suspended torsion balance  1  can be tracked in any allowed translational or rotational degree of freedom.  
         [0067]     In another possible implementation interferometric position read-out can be used to detect the position of the torsion balance  1 .  
         [0068]     The first optical module  24  of the optical readout device has a similar function, but it generates a light beam which is directed onto the first mirror  10  ( FIG. 1A ) of the torsion balance  1 .  
         [0069]     The light beam fed to the fiber outcoupler  26  via the optical fiber  27  is modulated (chopped) by an acousto-optical modulator (AOM) with a predetermined modulation frequency. Further, the detector  30  generates an electrical measurement signal which is fed to a lock-in amplifier (not shown) via a bandpass filter (not shown). Sending the electrical measurement signal generated by the detector  30  to the same lock-in amplifier as the modulation frequency the light beam generates a DC (direct current) signal out of exactly one frequency component of the detected electrical measurement signal. Now one assumes that the electrical measurement signal contains a lot of disturbing influences with a variety of different frequency components. Therefore, the optical readout device comprises a bandpass filter (not shown) filtering the electrical measurement signal before its amplification by the lock-in amplifier. The bandpass filter comprises a centre frequency corresponding to the modulation frequency which supports the lock-in technique.  
         [0070]     Further,  FIG. 4  shows a Faraday cage  33  consisting of aluminium, which encases the torsion balance  1 , so that the torsion balance  1  is shielded from electrostatic disturbances.  
         [0071]     Further, the entire apparatus apart from the first and second optical modules  24 ,  25  is encapsulated by a box  34  (see  FIG. 6 ) which is covered by a so-called μ-metal foil with a high magnetic permeability, so that the box  34  shields the torsion balance  1  from magnetic disturbances.  
         [0072]     Finally, FIG. 7  shows a vacuum housing  35  mounted on a base plate  36 . The base plate  36  is actually the top part of a commercially available active vibration isolation board. The vacuum housing  35  encapsulates the entire apparatus mentioned above in order to reduce thermal gradients which may cause “winds” around the setup. The latter could lead to disturbances in the measured signal. The low pressure within the vacuum housing  35  is realized by use of a vibration free ion pump, while the disturbing magnetic field of the pump is reduced to a reasonable amount by the above mentioned μ-metal shield. In order to avoid mechanically transmitted vibrations from the surrounding of the setup, the complete system is mounted on top of an active vibration isolation system.  
         [0073]     The actual measurement signal is given by the feedback voltage signal, which has to be applied to the first and second feedback electrodes  8 ,  9  in order to hold the torsion balance  1  in equilibrium.  
         [0074]     A typical measurement cycle includes initial damping cycles to compensate for residual motion following adjustment. After that, the detection of rotational modes of the torsion balance  1  is possible.  
         [0075]     The horizontal acceleration or gravity gradients, which act on the torsion balance  1  (precisely: the center of mass  12 ) can thus be detected with a very high precision. This is the result of the torsional suspension which is extremely sensitive to horizontal accelerations and allows for precise measurements.  
         [0076]     Vertical accelerations or gravity gradients can be detected with lower precision. The related motion is a common swinging mode of the torsion wire  3 , which is less sensitive than the torsional mode.  
         [0077]     In total, any applied gravitational force acting on the torsion balance  1 , can be decomposed into x-, y- and z-components, giving a true  3 -dimensional torsional gravimeter.  
         [0078]     Finally,  FIG. 8  shows a schematic of the optical readout device of the gravimeter described above.  
         [0079]     Firstly, the optical readout device of the gravimeter comprises a stabilized light input system  37  including a laser  38 , an acousto-optical modulator (AOM)  39  and a fiber in-coupler  40 . The laser  38  generates a DC light beam, i.e. a CW beam (CW—Continuous wave), which is modulated by the acousto-optical modulator  39  with a modulation frequency generated by a frequency reference  41 . In this embodiment, the modulation frequency is f=100 kHz. Thus, the acousto-optical modulator  39  generates an AC modulated light beam, which is fed to the fiber in-coupler  40 . The fiber in-coupler  40  couples the AC modulated light beam into the fiber  27  shown in  FIGS. 4 and 5 .  
         [0080]     Further, the optical readout device comprises a bandpass amplifier  42  having a centre frequency of 100 kHz, which corresponds to the modulation frequency generated by the frequency reference  41 . Therefore, the bandpass filter  42  filters the electrical measurement signal generated by the detector  30 , which supports the lock-in technique.  
         [0081]     The bandpass filtered measurement signal is then fed to a lock-in amplifier  43 , which also receives the modulation frequency f=100 kHz from the frequency reference  41 . Thus, the lock-in amplifier  43  generates a position signal indicating the angular position of the torsion balance  1  with regard to the rotation axis  5 .  
                         TABLE 1                       Index of Reference Numerals                                 1   Torsion balance        2   Rod        3   Torsion wire        4   Top of the rod        5   Rotation axis        6   Stick        7   Test mass        8   First feedback electrode        9   Second feedback electrodes       10   First mirror       11   Second mirror       12   Center of mass       13   Base       14   Column       15   Arm       16   First capacitor       17   Upper part of the housing       18   Lower part of the housing       19-22   Second capacitors       23   Base plate       24   First optical module       25   Second optical module       26   Fiber outcoupler       27   Optical fiber       28   Beamsplitter cube       29   Mirror       30   Detector       31   Base plate       32   Light beam       33   Faraday cage       34   Box       35   Vacuum housing       36   Base plate (antivibration device)       37   Stabilized light input system       38   Laser       39   Acousto-optical modulator       40   Fiber in-coupler       41   Frequency reference       42   Bandpass amplifier       43   Lock-in amplifier                  
 
         [0082]     Although preferred embodiments of the invention have been described in detail, it will be readily appreciated by those skilled in the art that further modifications, alterations and additions to the invention embodiments disclosed may be made without departure from the spirit and scope of the invention as set forth in the appended claims. For example, the acousto-optical modulator  39  may be replaced by an electro-optical modulator or a chopper without departing from the invention.