Abstract:
A gravimeter for detecting a gravity difference between two points is disclosed. The gravimeter comprises an interferometric arrangement wherein the length of a reference arm is dependent upon the gravity local to a first accelerometer and the length of a sample arm is dependent upon the gravity local to a second accelerometer. A pair of photodetectors that operate in complimentary fashion provide electrical signals based on a first signal conveyed by the reference arm and a second signal conveyed by the sample arm. A change in the differential gravity between the two points induces equal and opposite changes to the magnitudes of the two electrical signals.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This case claims priority to: U.S. Provisional Patent Application Ser. No. 61/037,661, filed Mar. 18, 2008 (Attorney Docket: 123-090US), which is incorporated by reference. 
         [0002]    If there are any contradictions or inconsistencies in language between this application and one or more of the cases that have been incorporated by reference that might affect the interpretation of the claims in this case, the claims in this case should be interpreted to be consistent with the language in this case. 
     
    
     FIELD OF THE INVENTION 
       [0003]    The present invention relates to gravimeters in general, and, more particularly, to gradient gravimeters. 
       BACKGROUND OF THE INVENTION 
       [0004]    Gravimetric sensing is a powerful tool for used in such applications as geological surveying, oil field exploration, earthquake detection, homeland defense, and shipping container shock detection. A gravimeter is an instrument used measuring a local gravitational field. A gravimeter is a highly sensitive type of accelerometer, specialized for measuring the constant downward acceleration of gravity. Gravimeters have better sensitivity than a conventional accelerometer, however, which enables them to measure very tiny fractional changes within the Earth&#39;s gravity. Such small changes in local gravity can be caused by, among other things, a geologic structure, a mass of highly dense material (e.g., nuclear material and its storage container), or the shape of the Earth. 
         [0005]    An absolute gravimeter provides an absolute value for gravity local to a position. A typical absolute gravimeter comprises a mass that is propelled upward to an apex, from which it subsequently free-falls. This is normally performed in a vacuum to mitigate the effects of air friction. Acceleration is determined based on the characteristics of the free-fall of the mass. In some prior-art gravimeters, the mass includes a retroreflector that terminates one arm of a Michelson interferometer. By counting and timing the interference fringes, the velocity and acceleration of the mass during free-fall can be determined. In some cases, the system measures both upward and downward motion of the mass, thereby enabling the cancellation of some systematic measurement errors. 
         [0006]    Two or more gravimeters can be used in unison to provide a relative measure of gravity over a region. Two- or three-dimensional mapping of a gravitational field can provide a great deal of information about sub-surface structure and materials. A sensor that is capable of precisely mapping the gradients in the gravitational field can offer a high degree of precision about the density profiles of nearby geological formations, such as mineral deposits or subterranean oil fields. 
         [0007]    The most common type of relative gravimeter is spring based. A spring-based relative gravimeter is basically a weight on a spring, and by measuring the amount by which the weight stretches the spring, local gravity can be determined. The spring must be carefully calibrated, however. This is typically done by placing the instrument in a location with a known gravitational acceleration. 
         [0008]    The high-sensitivity of a gravimeter makes it susceptible to extraneous vibrations. Numerous approaches have been used to attempt to mitigate the deleterious effects of such vibrations. For example, many gravimeters include integrated vibration isolation. Unfortunately, such isolation requires complex and expensive infrastructure and affords only partial isolation. Sophisticated post-measurement signal processing has also been applied to reduce the noise due to vibrations and improve signal-to-noise ratio (SNR). This requires, however, a highly developed model of the noise sources and also adds to the cost and complexity of the gravimeter system. Alternatively, since some applications do not require gravity measurements at high speed, attempts to improve SNR have included time-averaging the output of the device. Although time averaging offers improvement in gravimeter sensitivity, it precludes the use of such systems in many applications. 
       SUMMARY OF THE INVENTION 
       [0009]    The present invention provides a means for detecting a gravity gradient between two locations without some of the costs and disadvantages of the prior art. Some embodiments of the present invention are particularly well-suited for use in applications such as oil field exploration, mineral prospecting, and geological surveying. 
         [0010]    Some embodiments of the present invention comprise an interferometer arrangement that has a reference arm and a sample arm. The length of the reference arm is dependent upon the position of a first mirror that is physically coupled to a mass of a first accelerometer located at a first location. The length of the sample arm is dependent upon the position of a second mirror that is physically coupled to a mass of a second accelerometer located at a second location. The position of each mass and, therefore, the length of each of the reference and sample arms, is affected by the gravitational field local to its respective accelerometer. 
         [0011]    An input signal is split into a reference signal and a sample signal. The reference signal is conveyed through the reference arm to a first mirror at a first location. The sample optical signal is conveyed through the sample arm to a second mirror at a second location. The reference and sample signals are reflected from their respective mirrors to a beam splitter. The beam splitter distributes the reference signal into a first reference component on a first signal and a second reference component on a second signal. The beam splitter also distributes the sample signal into a first sample component on the first signal and a second sample component on the second signal. A phase shift of P radians is induced on the second sample component with respect to the first sample component. As a result, a change in the gravity difference between the first location and the second location induces changes to the intensity of the first signal that is equal and opposite to a change in the intensity of the second signal. 
         [0012]    In some embodiments, two-dimensional sensor modules are located at each of the first location and second location. As a result, such embodiments enable a measure of differential gravity in two dimensions between the two locations. 
         [0013]    In some embodiments, three-dimensional sensor modules are located at each of the first location and second location. As a result, such embodiments enable a measure of differential gravity in three dimensions between the two locations. 
         [0014]    In some embodiments, mechanical energy is conveyed between the sensors at the first location and the second location. As a result, such embodiments are less susceptible to noise due to shock, vibration, and external acceleration. 
         [0015]    In some embodiments, thermal energy is conveyed between the sensors at the first location and the second location. As a result, such embodiments are less sensitive to noise due to thermal gradients between the two locations. 
         [0016]    An embodiment of the present invention comprises a first interferometer, wherein the first interferometer comprises: a first reference arm having a first reference path length that is based on a first gravitational field, wherein the first reference arm conveys a first reference signal; a first sample arm having a first sample path length that is based on a second gravitational field, wherein the first sample arm conveys a first sample signal; a first beam splitter, wherein the first beam splitter distributes the first reference signal into a first signal and a second signal, and wherein the first beam splitter distributes the first sample signal into the first signal and the second signal; a first photodetector, wherein the first photodetector receives the first signal; and a second photodetector, wherein the second photodetector receives the second signal; wherein a change in the difference between the first reference path length and the first sample path length induces a first intensity change in the first signal and a second intensity change in the second signal, and wherein the first intensity change and the second intensity change are equal and opposite. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0017]      FIG. 1  depicts a schematic diagram of details of a differential gravimeter in accordance with an illustrative embodiment of the present invention. 
           [0018]      FIG. 2  depicts a method for sensing a gravity gradient between two locations in accordance with the illustrative embodiment of the present invention. 
           [0019]      FIG. 3  depicts a schematic drawing depicting details of an optical system in accordance with the illustrative embodiment of the present invention. 
           [0020]      FIG. 4A  depicts a top view of a sensor in accordance with the illustrative embodiment of the present invention. 
           [0021]      FIG. 4B  depicts a side view of a sensor in accordance with the illustrative embodiment of the present invention. 
           [0022]      FIG. 5  depicts a three-dimensional differential gravimeter in accordance with an alternative embodiment of the present invention. 
           [0023]      FIG. 6  depicts a method for sensing gravity gradients between two locations, in three-dimensions, in accordance with the alternative embodiment of the present invention. 
           [0024]      FIG. 7  depicts a multi-wavelength source in accordance with the alternative embodiment of the present invention. 
           [0025]      FIG. 8  depicts multi-wavelength sensor module  514 - 1 . 
           [0026]      FIG. 9  depicts multi-wavelength detection module  532 - 1 . 
       
    
    
     DETAILED DESCRIPTION 
       [0027]      FIG. 1  depicts a schematic diagram of details of a differential gravimeter in accordance with an illustrative embodiment of the present invention. Gravimeter  100  comprises source  102 , beam splitter  106 , sensors  116 - 1  and  116 - 2 , photodetectors  134  and  138 , processor  142 , and frame  146 . 
         [0028]    Gravimeter  100  provides an output signal based on a difference in a first gravitational field at location L 1  that is aligned with the z-direction and a second gravitational field at location L 2  that is aligned with the z-direction. For the purposes of this specification, including the appended claims, the axes and/or directions are “aligned” if they are collinear, or if they are non-collinear but are substantially parallel. 
         [0029]      FIG. 2  depicts a method for sensing a gravity gradient between two locations in accordance with the illustrative embodiment of the present invention. Method  200  is described with continuing reference to  FIG. 1 . 
         [0030]      FIG. 3  depicts a schematic drawing depicting details of an optical system in accordance with the illustrative embodiment of the present invention. Optical system  300  depicts the optical system of gravimeter  100 .  FIG. 3  is described with continuing reference to  FIGS. 1 and 2 . Optical system  300  comprises reference arm  110 , sample arm  114 , detector arm  302 , and detector arm  304 . 
         [0031]    Source  102  provides input signal  104 , which is substantially monochromatic light. Input signal  104  passes through circulator  136  and is received by beam splitter  106 . It will be clear to one skilled in the art how to make, use, and specify source  102 , beam splitter  106 , and circulator  136 . 
         [0032]    Method  200  begins with operation  201 , wherein beam splitter  106  distributes the optical energy of input signal  104  and equally into input reference signal  108  on reference arm  110  and input sample signal  112  on sample arm  114 . 
         [0033]    Reference signal  108  is described as electric field: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
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         [0000]    where E 0 , ω, and λ are the maximum intensity, frequency, and wavelength, respectively, of input signal  104 , and x is the propagation distance from beam splitter  106 . 
         [0034]    In similar fashion, sample signal  112  is described as electric field: 
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         [0035]    Input reference signal  108  and input sample signal  112  are coherent signals as they leave beam splitter  106 . In some embodiments, input signal  104  is distributed unequally into input reference signal  108  and input sample signal  112 . 
         [0036]    Reference arm  110  conveys input reference signal  108  to sensor  116 - 1 . Reference arm  110  comprises turning mirror  306 , which aligns input reference signal  108  with the z-direction. 
         [0037]    Sample arm  114  conveys input sample signal  112  to sensor  116 - 2 . Sample arm  114  comprises turning mirrors  308  and  310 , which align input sample signal  112  with the z-direction. 
         [0038]    It should be noted that the use of the terms “reference” and “sample,” as used herein, are assigned arbitrarily and serve only to conveniently distinguish one path and set of signals from the other. One skilled in the art will recognize that, for example, arm  110  could have been designated as the sample and arm  114  could have been designated as the reference arm. 
         [0039]    At operation  202 , sensor  116 - 1  receives input reference signal  108  and reflects it back through reference arm  110  as reference signal  118 . 
         [0040]    The path length PL 1  of reference arm  110  is the combined distance traveled by input reference signal  108  and reference signal  118 . In other words, path length PL 1  is equal to twice the distance between beam splitter  106  and sensor  116 - 1 . 
         [0041]    At operation  203 , sensor  116 - 2  receives input sample signal  112  and reflects it back through sample arm  114  as sample signal  120 . 
         [0042]    The path length PL 2  of sample arm  114  is the combined distance traveled by input sample signal  112  and sample signal  120 . In other words, path length PL 2  is equal to twice the distance between beam splitter  106  and sensor  116 - 2 . 
         [0043]    Sensors  116 - 1  and  116 - 2  are attached to frame  146  at locations L 1  and L 2 , respectively. Locations L 1  and L 2  are separated by distance D. Typically distance D is within the range of approximately 0.5 meters (m) to approximately 3 m. 
         [0044]    Frame  146  is a mechanically rigid frame suitable for conveying mechanical energy between sensors  116 - 1  and  116 - 2 . In some embodiments, frame  146  conveys thermal energy between sensors  116 - 1  and  116 - 2 . In some embodiments, frame  146  conveys both mechanical energy and thermal energy between sensors  116 - 1  and  116 - 2 . By virtue of the fact that frame  146  conveys energy between sensors  116 - 1  and  116 - 2 , external vibrations, accelerations, shocks, temperature changes, etc., are common to both sensors. As a result, gravimeter  100  can have an improved SNR. In some embodiments, frame  146  is not included. 
         [0045]      FIGS. 4A and 4B  depict a top view and side view of a sensor in accordance with the illustrative embodiment of the present invention. Sensor  116  is representative of each of sensors  116 - 1  and  116 - 2 .  FIG. 4  is described with continuing reference to  FIGS. 1 ,  2 , and  3 . 
         [0046]    It should be noted that sensor  116  is merely one example of a sensor suitable for use in gravimeter  100 . One skilled in the art will recognize that the present invention merely requires a sensor that comprises a mirror whose position is based on the gravitational field local to the sensor&#39;s location. 
         [0047]    Sensor  116  comprises mass  402 , tethers  404 - 1  through  404 - 4 , mirror  408 , and bulkhead  410 . 
         [0048]    Mass  402  is a rigid block of material having a known mass. Mass  402  is attached to bulkhead  410  by tether system  406 . Mass  402  comprises mirror  408 , which is disposed on the bottom surface of mass  402 . The position of mirror  408 , with respect to mass  402 , depends upon the optical system used to interrogate it. In some embodiments, mirror  408  is disposed on the top surface of mass  402 . In some embodiments a mirror  408  is disposed on both the top and bottom surfaces of mass  402 . 
         [0049]    Tether system  406  comprises tethers  404 - 1  through  404 - 2  (collectively referred to as tethers  404 ). Each of tethers  404  is a resilient element that enables motion of mass  402  along axis  412 , which is aligned with the z-direction, as shown. 
         [0050]    The specific shapes and sizes of mass  402 , mirror  408 , and tether system  406  are design considerations that are application dependent. For most applications, mass  402  has a circular or square shape having a diameter or width within the range of approximately 0.5 millimeters (mm) to approximately 20 mm. The illustrative embodiment depicts an exemplary design comprising: a mass and a tether system comprising four tethers; The mass having a square shape of approximately 15 mm on a side and a thickness of approximately 1 mm; each tether having a length of approximately 10 mm and a thickness of 0.1 mm and a width of 0.1 mm. Further, although the illustrative embodiment comprises four tethers  404 , it will be clear to one skilled in the art, after reading this specification, how to specify, make, and use embodiments of the present invention wherein sensor  116  comprises any number of tethers  404 . 
         [0051]    Suitable materials for mass  402 , frame  146 , and tether  406  include, without limitation, semiconductors, semiconductor compounds, dielectrics, glasses, polymers, ceramics, metals, and composite materials. In some embodiments, mass  402 , frame  146 , and tether  406  are formed from a continuous layer of material. 
         [0052]    In the illustrative embodiment, mirrors  408 - 1  and  408 - 2  are separated from beam splitter  106  by the same distance. When the gravitational field at location L 1  is equal to the gravitational field at location L 2 , the position of mass  116 - 1  along axis  412 - 1  is equal to the position of mass  116 - 2  along axis  412 - 2 . PL 1  and PL 2 , therefore, are equal. 
         [0053]    In some embodiments, sensors  116 - 1  and  116 - 2  are separated from beam splitter  106  by different distances and PL 1  and PL 2  have different path lengths when the gravitational fields at locations L 1  and L 2  are the same. In such embodiments, therefore, the phases of reference sample  118  and sample signal  120 , as received by beam splitter  106 , are out of phase by an amount based on the difference in their path lengths. Such embodiments can have greater sensitivity to wavelength noise than the illustrative embodiment, however. 
         [0054]    In some embodiments sensors  116 - 1  and  116 - 2  are in opposing orientation along the z-direction. In some embodiments, sensors  116 - 1  and  116 - 2  are in the same orientation along the z-direction. In some embodiments, a gravitational field that is relatively greater at location L 2  results in an increase in path length PL 2  relative to path length PL 1 . In some embodiments, a gravitational field that is relatively greater at location L 2  results in a decrease in path length PL 2  relative to path length PL 1 . 
         [0055]    At operation  204 , beam splitter  106  receives reference signal  118  and distributes it equally into first signal  130  on detector arm  302  and second signal  132  on detector arm  304 . In operation  204 , beam splitter  106  reflects reference component  122  to photodetector  134  and passes reference component  124  to photodetector  134 - 2 . 
         [0056]    At operation  205 , beam splitter  106  receives sample signal  120  and distributes it equally into first signal  130  on detector arm  302  and second signal  132  on detector arm  304 . In operation  205 , beam splitter  106  reflects sample component  128  to photodetector  134 - 2  and passes sample component  126  to photodetector  134 . 
         [0057]    Reference component  124  and sample component  128  (i.e., second signal  132 ) are directed toward photodetector  134 - 2  by turning mirror  136 . 
         [0058]    Reference component  122  and sample component  126  combine as first signal  130 , which has an electric field described as: 
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         [0000]    where φ 1 =2ΠPL 1 /λ, and φ 2 =2ΠPL 2 /λ. Equation (3) can be further expanded to: 
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         [0059]    In similar fashion, reference component  124  and sample component  128  combine as second signal  132 , which has an electric field described (in expanded form) as: 
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         [0060]    It is an aspect of the present invention that optical system  300  induces the Π radian difference between the relative phases of the components of first signal  130  and the relative components of second signal  132 . First signal  130  and second signal  132 , therefore, are complimentary signals wherein a change in the intensity of one must be matched by an equal and opposite change in the intensity of the other. By detecting and comparing first signal  130  and second signal  132 , as discussed below, gravimeter  100  can have improved sensitivity as compared to conventional differential gravimeters. 
         [0061]    It should be noted that the present invention still provides a sensitivity improvement over the prior art when the difference in the relative phase differences between the components of first signal  130  and second signal  132  is not exactly Π radians, as long as the difference has a magnitude that is between Π/2 and 3Π/2. In some embodiments, therefore, optical system  300  induces a difference in the relative phase differences between the components of first signal  130  and second signal  132  that is within the range of (n+1/2)*Π to (n+3/2)*Π. 
         [0062]    In some embodiments, the path lengths of reference arm  110 , sample arm  114 , detector arm  302 , and detector arm  304  are such that reference component  122  and sample component  125  have a relative phase difference of n*Π, wherein n is a negative or positive integer. In some embodiments, the path lengths of reference arm  110 , sample arm  114 , detector arm  302 , and detector arm  304  are such that reference component  124  and sample component  128  have a relative phase difference of n*2Π, wherein n is a negative or positive integer. 
         [0063]    In operation, the position of mirror  408 - 1  is a function of the local gravity at sensor  116 - 1  (i.e., at location L 1 ). As a result, the phase of reference component  122  at photodetector  134  and the phase of reference component  124  at photodetector  134 - 2  are based on the local gravity at sensor  116 - 1 . 
         [0064]    In similar fashion, the position of mirror  408 - 2  is a function of the local gravity at sensor  116 - 2  (i.e., at location L 2 ). As a result, the phase of sample component  124  at photodetector  134  and the phase of sample component  128  at photodetector  134 - 2  are also based on the local gravity at sensor  116 - 2 . 
         [0065]    By virtue of the fact that the relative phases of the signals of first signal  130  and the relative phases of the signals of second signal  132  are different by Π radians, first signal  130  and second signal  132  are complimentary signals that contain all of the optical energy of input signal  102  (disregarding optical losses through optical system  300 ). As a result, a decrease in intensity of one of the signals is matched by a commensurate increase in intensity of the other signal. 
         [0066]    When the gravitational field in the z-direction at location L 2  becomes different than the gravitational field in the z-direction at location L 1 , mass  402 - 2  moves to a different position along axis  412 - 2 . This changes the length of sample path length P 2 , which thereby changes the phase of sample signal  120  as received by beamsplitter  106 . As a result, the phases of sample components  126  and  128  at photodetectors  134  and  134 - 2  also change. Since sample components  126  and  128  are out of phase by Π radians at their respective photodetectors, the intensities of first signal  130  and second signal  132  change by equal and opposite amounts. 
         [0067]    At operation  206 , photodetector  134  generates electrical signal  138  based on the intensity of first signal  130 . 
         [0068]    At operation  207 , photodetector  134 - 2  generates electrical signal  140  based on the intensity of second signal  132 . Photodetectors  134  and  134 - 2  operate in complimentary fashion, wherein a decrease in the magnitude of one of electrical signals  138  and  140  is matched by an increase in the magnitude of the other one of electrical signals  138  and  140 . 
         [0069]    At operation  208 , processor  142  generates output  144  based on electrical signals  138  and  140 . Since electrical signals  138  and  140  are complimentary, a change in the magnitude of output signal  144  is twice as large as a change in the magnitude of either of the electrical signals. Gravimeter  100 , therefore, has twice the sensitivity of a conventional differential gravimeter. 
         [0070]      FIG. 5  depicts a three-dimensional differential gravimeter in accordance with an alternative embodiment of the present invention. Gravimeter  500  comprises multi-wavelength source  502 , beam splitter  106 , multi-axis sensor modules  514 - 1  and  514 - 2 , and multi-wavelength detection modules  532 - 1  and  532 - 2 . Gravimeter  500  enables gravity gradients to be sensed along the x-, y-, and z-directions, wherein the x-, y-, and z-directions are mutually orthogonal. 
         [0071]      FIG. 6  depicts a method for sensing gravity gradients between two locations, in three-dimensions, in accordance with the alternative embodiment of the present invention. Method  600  begins with operation  601 , wherein wavelength-division multiplexed (WDM) input signal  504  is provided by multiplexing input signals  104 -X,  104 -Y, and  104 -Z. 
         [0072]      FIG. 7  depicts a multi-wavelength source in accordance with the alternative embodiment of the present invention. Multi-wavelength source  502  comprises source  102 -X,  102 -Y, and  102 -Z, which provide input signals  104 -X,  104 -Y, and  104 -Z, respectively, and multiplexor  702 . Each of input signals  104 -X,  104 -Y, and  104 -Z is characterized by a unique wavelength. 
         [0073]    Multiplexor  702  is a conventional optical element for multiplexing a plurality of signals having different wavelengths into a single WDM signal. Multiplexor  702  combines input signals  104 -X,  104 -Y, and  104 -Z into WDM input signal  504 . 
         [0074]    At operation  602 , beam splitter  106  receives WDM input signal  504  and distributes its optical energy equally into WDM input reference signal  506  and WDM input sample signal  508 . 
         [0075]    At operation  603 , multi-wavelength sensor module  514 - 1  receives WDM input reference signal  506  and demultiplexes it by wavelength into input reference signals  108 -X,  108 -Y, and  108 -Z. 
         [0076]      FIG. 8  depicts multi-wavelength sensor module  514 - 1 . Sensor module  514 - 1  comprises sensors  116 - 1 X,  116 - 1 Y, and  116 - 1 Z, and wavelength distributor  702 - 1 . Sensor module  514 - 1  is representative of sensor module  514 - 2 . Sensor module  514 - 1  is representative of sensor module  514 - 2 ; however, sensor module  514 - 2  comprises sensors  116 - 2 X,  116 - 2 Y, and  116 - 2 Z, and distributor  802 - 2 . 
         [0077]    Distributor  802 - 1  is a conventional optical element for Demultiplexing a WDM signal into a plurality of signals having different wavelengths. Distributor  802 - 1  separates WDM input reference signal  506  into input reference signals  108 -X,  108 -Y, and  108 -Z and provides them to sensors  116 - 1 X,  116 - 1 Y, and  116 - 1 Z, respectively. In some embodiments, wavelength distributor  802 - 1  comprises one or more chromatic beam splitters. 
         [0078]    Operation of each of sensors  116 - 1 X,  116 - 1 Y, and  116 - 1 Z is analogous to the operation of sensor  116 - 1  of gravimeter  100 , wherein sensor  116 - 1 X (i.e., axis  412 - 1 X) is aligned with the x-direction, sensor  116 - 1 Y is aligned with the y-direction, and sensor  116 - 1 Z is aligned with the z-direction. For example, sensor  116 - 1 X comprises mirror  408 - 1 X, whose position along axis  412 - 1 X is based on the gravitational field along the x-direction at location L 1 . 
         [0079]    Each of sensors  116 - 1 X,  116 - 1 Y, and  116 - 1 Z reflects its corresponding input reference signal as a reference signal. For example, sensor  116 - 1 X reflects input reference signal  108 -X back to distributor  802 - 1  as reference signal  118 -X. 
         [0080]    At operation  605 , reference signals  118 -X,  118 -Y, and  118 -Z are recombined at distributor  802 - 1  to form WDM reference signal  516 . Since the distance between beam splitter  106  and distributor  802 - 1  is fixed, each of path lengths PL 3 -X, PL 3 -Y, and PL 3 -Z is based on the position of each of mirrors  408 - 1 X,  408 - 1 Y, and  408 - 1 Z, respectively. 
         [0081]    In similar fashion, wavelength distributor  802 - 2  separates WDM input sample signal  508  into input sample signals  112 -X,  112 -Y, and  112 -Z and provides them to sensors  116 - 2 X,  116 - 2 Y, and  116 - 2 Z, respectively. 
         [0082]    Each of sensors  116 - 2 X,  116 - 2 Y, and  116 - 2 Z reflects its corresponding input sample signal as a sample signal. For example, sensor  116 - 2 X reflects input sample signal  112 -X back to distributor  802 - 2  as sample signal  120 -X. 
         [0083]    At operation  606 , sample signals  120 -X,  120 -Y, and  120 -Z are recombined at distributor  802 - 1  to form WDM sample signal  516 . Since the distance between beam splitter  106  and distributor  802 - 2  is fixed, each of path lengths PL 4 -X, PL 4 -Y, and PL 4 -Z is based on the position of each of mirrors  408 - 2 X,  408 - 2 Y, and  408 - 2 Z, respectively. 
         [0084]    At operation  607 , beam splitter  106  distributes the optical energy in WDM reference signal  516  equally into WDM first signal  528 . 
         [0085]    At operation  608 , beam splitter  106  distributes the optical energy in WDM sample signal  518  equally into WDM second signal  530 . 
         [0086]      FIG. 9  depicts multi-wavelength detection module  532 - 1 . Detection module  532 - 1  comprises distributor  802 - 3  and photodetectors  134 - 1 X,  134 - 1 Y, and  134 - 1 Z. Detection module  532 - 1  is representative of detection module  532 - 2 ; however, detection module  532 - 2  comprises sensors  116 - 2 X,  116 - 2 Y, and  116 - 2 Z, and distributor  802 - 4 . 
         [0087]    At operation  609 , distributor  802 - 3  separates WDM first signal  528  into first signals  130 -X,  130 -Y, and  130 -Z and provides them to photodetectors  134 - 1 X,  134 - 1 Y, and  134 - 1 Z, respectively. Also at operation  609 , distributor  802 - 4  separates WDM second signal  530  into second signals  132 -X,  132 -Y, and  132 -Z and provides them to photodetectors  134 - 2 X,  134 - 2 Y, and  134 - 2 Z, respectively. 
         [0088]    At operation  610 , photodetectors  134 - 1 X,  134 - 1 Y, and  134 - 1 Z generate electrical signals  138 - 1 X,  138 - 1 Y, and  138 - 1 Z, respectively. Also at operation  610 , photodetectors  134 - 2 X,  134 - 2 Y, and  134 - 2 Z generate electrical signals  138 - 2 X,  138 - 2 Y, and  138 - 2 Z, respectively. 
         [0089]    In analogous fashion to gravimeter  100 , processor  142  receives electrical signals  138 - 1 X,  138 - 1 Y,  138 - 1 Z,  138 - 2 X,  138 - 2 Y, and  138 - 2 Z and provides an output signal for the differential gravity along the x-, y-, and z-directions between locations L 1  and L 2 . 
         [0090]    Although gravimeter  500  is a three-dimensional gravimeter, it will be clear to one skilled in the art, after reading this specification, how to make and use alternative embodiments of the present invention that are two-dimensional gravimeters. 
         [0091]    Further, it will be clear to one skilled in art how to make two- and three-dimensional gravimeters wherein the axes of sensitivity are not orthogonal. 
         [0092]    It is to be understood that the disclosure teaches just one example of the illustrative embodiment and that many variations of the invention can easily be devised by those skilled in the art after reading this disclosure and that the scope of the present invention is to be determined by the following claims.