Patent Application
20140026654
This invention relates to measuring a characteristic of gravity, and more specifically, to a new and improved differential gradiometer and method which directly measures a differential gradient of gravity, i.e. a gradient of a gradient of gravity or a second spacial derivative of gravity in the vertical direction, without the necessity to first obtain multiple gravity measurements and gravity gradient measurements from which to calculate the differential gradient of gravity. In addition, the present invention relates to a differential gradiometer and method which employs multiple test masses and multiple light beams which interact advantageously with the test masses to remove or cancel large background gravity and gravity gradient signals caused by the earth itself, thereby making it easier to detect the differential gradient of gravity caused by near field mass-variation sources like high density mineral and ore deposits or low density voids and tunnels, while simultaneously enhancing the accuracy of the measurement and facilitating use of the invention on dynamic platforms such as marine vessels and aircraft.
Gravity is the force of inherent natural attraction between two massive bodies. The magnitude of the gravitational force is directly related to the mass of the bodies and is inversely related to the square of the distance between centers of mass of the two attracted bodies.
Gravity is measured as acceleration, g, usually as a vertical vector component. The freefall acceleration, g, of an object near the surface of the earth is given to a first approximation by the gravitational attraction of a point with the mass of the entire earth, Me, located at the center of the earth, a distance, Re, from the surface of the earth. This nominal gravity value, g=G×Me/Re2, is about 9.8 m/s2. Thus, the freefall acceleration due to gravity near the earth's surface of an object having a small mass compared to the mass of the earth is about 9.8 m/s2. The common unit of measurement for gravity is the “Galileo” (Gal), which is a unit of acceleration defined as 1 cm/s2. One Gal generally approximates 1/1000 (10−3) of the force of gravity at the earth's surface. An instrument used to measure gravity is called a “gravimeter.”
The most accurate gravimeters are absolute gravimeters. Interferometric absolute gravimeters usually use a freely falling test mass and a laser or single-frequency light beam which reflects from the freely falling test mass. The reflected light beam is combined with a reference light beam to develop interference fringes. Interference fringes are instances where the amplitude or intensity of the reflected and reference light beams add together to create increased intensity, separated by instances where the two beams cancel or create diminished intensity.
Fringes occur on a periodic basis depending upon the change in the optical path length of the reflected beam relative to the optical path length of the reference beam. One fringe occurs whenever the optical path difference between the reflected and reference beams changes by the wavelength of the light of the two beams. When an object that is part of the beam path moves, it typically changes the path length by twice the amount of physical movement because the physical movement changes the both the entry and exit of the beam path. In this circumstance, a fringe typically occurs when the object moves by one-half of a wavelength. The fringes taken together as a set comprise a record of the distance that the freely falling body moves.
Because the path length of the reflected beam changes as it is reflected from the freely falling test mass, and because the freefall movement of the test mass is established by gravity, the occurrence and timing of the resulting interference fringes defines the characteristic of gravity. The use of optical fringe interferometry to measure gravity characteristics is well-known. U.S. Pat. No. 5,351,122 describes an example of an absolute gravity measuring instrument, called a “gravimeter.”
A gradient of gravity is the rate at which gravity changes in a certain direction and over a certain distance. A gravity gradient is therefore the change or first derivative of the gravity over distance. Near-field variations in gravity are caused by localized variations in the mass or density of at least one of the two attracted bodies. An instrument used to measure a gradient of gravity is called a “gradiometer.”
Although the gradient of gravity can be determined in any direction, the vertical gradient of gravity is useful in many practical applications. Vertical gravity gradients identify changes in density or mass of a particular material or geological structure. For example, gravity gradients are used to establish the location of underground geological structures, such as a pool of liquid petroleum encased within an earth formation, narrow seams or “tubes” of high density geological materials such as diamonds or cobalt, or voids in a geographical formation caused by a tunnel or cavern. These changes in the subterranean material density are most measurable within a relatively short near-field distance, typically within a few hundred meters.
Subsurface density anomalies, for example from valuable nearby high density ore bodies or voids caused by tunnels or areas of low density material, affect the local value of gravity, g, at a level of about 1 part per million (1/106), and in some cases 1 part per billion (1/109). The large background of the earth's gravity requires that any direct gravity measurement to detect such subsurface anomalies have a very large dynamic range of parts per billion, otherwise direct gravity measurements will not be useful for locating and detecting such subsurface density anomalies. It is difficult to make gravimeters with such levels of extremely high precision, so it is desirable to find ways to cancel the large effect of the earth's gravity while preserving the ability to detect gradations in nearby density anomalies.
The vertical gravity gradient of the earth is typically measured in terms of a unit called the Eotvos unit, E, given by 10−9/s2. The vertical gravity gradient of the entire earth is typically about 3000E. Typical nearby mass anomalies can affect the vertical gravity gradient at a level of about 1E or more. Thus, the contrast of the vertical gravity gradient caused by nearby mass anomalies to the earth's vertical gravity gradient is about 300,000 (3×105) times larger than for the gravity value itself. This means that a vertical gravity gradiometer can have 3×105 times less precision than a gravimeter and still be used effectively to detect or locate nearby mass or density anomalies.
A gradiometer removes the effect of gravity. Logically, a gradiometer differences the gravity measurements at two different nearby locations. A known vertical gravity gradiometer is made by placing two gravimeters above one other with a vertical separation of fixed distance, z, and then subtracting the two gravity measurements, g1 and g2. The vertical gravity gradient, γ, is then given by the ratio of this difference divided by the vertical separation, i.e. γ=(g2−g1)/z. This quantity is also mathematically referred to as the spatial derivative of gravity in the vertical direction.
This concept can be extended again by measuring the gradient, change or differential in the gradient of gravity. This gradient, change or differential in the gravity gradient is essentially the gradient of the gradient of gravity, referred to herein as the “differential gradient.” In a vertical sense, the differential gradient can be thought of as the spatial derivative of the gravity gradient in the vertical direction, i.e. ζ=(γ2−γ1)/z. Obtaining the differential gradient of gravity has the effect of removing the effect of the relatively large inherent gradient of gravity throughout the earth in the measurement. An instrument which measures the differential gradient of gravity is referred to herein as a “differential gradiometer.”
The differential gradient of gravity can be measured by mathematically subtracting two gravity gradient measurements and dividing the result by the separation distance of the two gravity gradient measurements. A single gradiometer can be used to measure the gravity gradient at two different locations, typically one above the other. Another way to measure the differential gradient of gravity is to use one or more absolute gravimeters. The gravity is measured at multiple locations, the measured gravity measurements are subtracted and then the result is divided by the distance between the locations of the two gravity measurements to obtain a gravity gradient measurement. The process is repeated at another location to obtain a second gravity gradient measurement at that other location. Then the pair of gradient measurements are subtracted and the result is divided by the distance between the locations where the two gradient measurements were obtained, to obtain the differential gradient of gravity over the distance between those locations.
The separate gravity measurements and gravity gradient measurements can be obtained approximately simultaneously with multiple instruments or at separated time intervals with the same instrument if the gravity and gravity gradient is not expected to change significantly between the times of the multiple measurements. The distance between the locations of these separate measurements is also measured. Each of these multiple separate measurements involves some risk and amount of error.
Each gravimeter and gradiometer used in measuring gravity and the gradient of gravity is also subject to naturally-occurring and man-made vibrations and other physical perturbations. These vibrations and perturbations cause minute changes in the path length of the reflected and reference light beams in a light beam interferometric instrument, causing interference fringes which are not related to the gravity characteristic measured. Such anomalous interference fringes reduce the accuracy of the measurement and enhance the potential for errors. Further still, each of the instruments is subject to unique vibrations and physical perturbations, which magnify the range of error when the measurements are subtracted from one another.
Attempts have been made to eliminate the anomalous vibration and perturbation errors through common mode rejection. In theory, connected-together instruments are subject to the same physical influences, thereby introducing the same error into all the measurements. When the measurements are subtracted, the common error in both signals is theoretically canceled or rejected. However, the practical effect falls substantially short of complete common mode rejection.
It is practically impossible to achieve a sufficiently rigid connection between the two instruments to cause both to experience the same degree of perturbation. It is impossible to freefall the test masses of the instruments at the same time, so each measurement is always subject to anomalies that do not influence the other measurement. The environments in which the test masses fall in the separate instruments are not the same, despite the attempt to create a vacuum around the test masses in the instruments. The vacuum surrounding each test mass has a slightly different amount of residual gas which creates a slightly different aerodynamic drag on each freefalling test mass. The different amounts of aerodynamic drag influence the freefall characteristics of each test mass differently, thereby introducing discrepancies. Further still, the optics which conduct the light beams in the connected instruments are slightly different, and those differences introduce unique discrepancies. Even slight changes in temperature or pressure may affect the optics of each instrument differently. Physical movement caused by vibration or perturbation of the external optical fibers or elements which conduct the input and output light beams into and from each instrument introduce unique phase shifts, which also influence the measurements. Separate laser light sources for each instrument create unique phase changes in the light beams, which introduce anomalous fringe effects that may introduce measurement errors. Inadvertent slight angular rotation or tilting of one or both the test masses during simultaneous freefall changes the length of the reflected light paths in that instrument, which again contributes to error when the two gravity or gravity gradient measurements are subtracted to determine the differential gradient of gravity.
These and other unique and adverse influences increase the possibility of deriving inaccurate measurements. In addition, the mathematical manipulations of subtracting the measurements and dividing by the distance between the measurement locations may compound the errors. These and other errors are not subject to common mode rejection, because the errors uniquely affect some singular aspect of one instrument and not any other instrument used. The inability to achieve effective common mode rejection makes the measurement of the differential gradient of gravity using gravimeters and gradiometers error-prone, particularly in vibration-prone or perturbation-prone environments.
This invention permits the direct measurement of the differential gradient of gravity, the gradient of the gradient of gravity, or the second spatial derivative of gravity, without the need to use gravimeters or gradiometers to make independent measurements at different times under different conditions, and then mathematically calculate the value of the differential gradient of gravity from the multiple separate measurements. The effects of background gravity and the background gravity gradient of the earth are inherently eliminated during the measurement, thereby greatly facilitating the detection of near field mass-variation sources such as high-density mineral or ore deposits or ore low-density underground voids or tunnels. The invention achieves a significantly enhanced signal-to-noise ratio when measuring the differential gradient of gravity caused by such near field sources, making the measurements easier to accomplish and more reliable.
In addition, the invention solves or ameliorates many of the known problems or disadvantages of using optical interferometric gravity or acceleration measuring instruments with freely falling test masses to obtain gravity- or acceleration-related measurements. A high level of common mode rejection of a variety of error-inducing adverse influences is achieved, including those caused by compounding errors from separate measurements when making mathematical calculations, and those caused from differences in path length of reflected and reference light beams, from physical perturbation and vibration, from variance in angular rotation of falling test masses, from differences in atmospheric composition of separate vacuum chambers, from differences caused by pressure and temperature changes, and from other things. The improvements of the invention, coupled with its single direct measurement capability, makes the invention practical to use in moving land, sea, air and space vehicles, as well as in many other commercial and industrial applications. These and other features and benefits are achieved by different aspects of the invention, which are generally summarized below.
One aspect of the invention pertains to a differential gradiometer for measuring a differential in gradients of gravity between two predetermined separated locations by interferometry of first and second light beams. First, second and third test masses are released for simultaneous freefall solely under the influence of gravity with the first and second test masses at one of the separated locations and the second and third test masses at the other one of the separated locations. An arrangement of optical elements directs the first and second light beams into first and second separate beam arms, respectively. The first beam arm directs the first light beam to impinge upon and reflect from the first and second test masses during simultaneous freefall of all three test masses, and the second beam arm directs the second light beam to impinge upon and reflect from the second and third test masses during simultaneous freefall of all three test masses. An interferometric combination of the first and second light beams delivered from the first and second beam arms after impingement upon and reflection from the test masses directly defines the differential gradient of gravity.
Another aspect of the invention involves a method of measuring a differential in gradients in gravity between two predetermined separated locations. First, second and third test masses freefall simultaneously under the influence of gravity. The first and second test masses freefall at one of the separated locations, and the second and third test masses freefall at the other one of the separated locations. A first light beam in a first beam arm is directed to impinge upon and reflect from the first and second test masses during simultaneous freefall of the three test masses, and a second light beam in a second beam arm is directed to impinge upon and reflect from the second and third test masses during simultaneous freefall of the three test masses. The first and second light beams from the first and second beam arms are combined while the first and second light beams impinge upon and reflect from the test masses during simultaneous freefall of the three test masses. The differential gradient of gravity is directly determined from interference characteristics resulting from the combination of the first and second light beams.
Subsidiary features of one or both of these aspects of the invention include some or all of the following. The optical path lengths of the two beam arms at one point in the simultaneous freefall of the three test masses is equal. An initial finite velocity is established on one of the test masses compared to the other two test masses at the instant of commencement of simultaneous freefall of the three test masses. The optical path lengths of the first and second beam arms change equally during any rotation of the second mass during freefall and remain unchanged with any rotation of either of the first and third test masses during freefall, thereby avoiding adverse influences from inadvertent rotation of the test masses. Optical centers of retroreflectors of the test masses are positioned relative to the center of mass of the test masses to avoid changing the optical path length or to create equal changes in the optical path lengths. The three test masses freefall in collinear, parallel and preferably vertically spaced paths, and the substantial majorities of the first and second beam arms are parallel to one another and parallel to the paths in which the test masses freefall. A single constant frequency input light beam may be used to create the first and second light beams, or separate constant frequency light beams can be used as the first and second light beams. All three test masses fall in a single vacuum chamber.
A more complete appreciation of the present invention and its scope may be obtained from the accompanying drawings, which are briefly summarized below, from the following detailed description of presently preferred embodiments of the invention, and from the appended claims.
The present invention involves an optical interferometric differential gradiometer 20, shown in
The slightly greater gravity on the lower test mass 24 causes it to experience a slightly greater downward acceleration compared to the downward acceleration of the middle test mass 23, and the slightly greater gravity on the middle test mass 23 causes it to experience a slightly greater downward acceleration compared to the upper test mass 22, during simultaneous freefall. The slightly different accelerations cause the lower test mass 24 to increase its downward velocity slightly more than the downward velocity of the middle test mass 23 and cause the middle test mass 23 to increase its downward velocity slightly more than the downward velocity of the upper test mass 22 during simultaneous freefall, thereby slightly increasing the physical separation between the test masses 23 and 24 compared to the physical separation between the test masses 23 and 22 at the end of their simultaneous freefall, compared to the physical separations of the test masses 22, 23 and 23, 24 at the beginning of their simultaneous freefall. An elevator 29, an elevator frame 30 and support devices 31 support the test masses 22, 23 and 24, release the test masses to fall freely solely under the influence of gravity, and catch the test masses at the end of their simultaneous freefall.
Two light beams 26 and 28 impinge upon and reflect from of the test masses 22, 23 and 24 while they fall freely within a vacuum chamber 27. The light beam 26 impinges upon and reflects from the test masses 23 and 24, and the light beam 28 impinges upon and reflects from test masses 22 and 23. The light beams 26 and 28 traverse the interior of the vacuum chamber 27 over optical paths referred to herein as beam arms 32 and 34, respectively. The beam arm 32 is oriented to cause the light beam 26 to impinge on and reflect from the test masses 23 and 24, and the beam arm 34 is oriented to cause the light beam 28 to impinge on and reflect from the test masses 22 and 23. Both light beams 26 and 28 in both beam arms 32 and 34 impinge on and reflect from the middle test mass 23. Accordingly, the test masses 22 and 23 therefore constitute one reflection pair of test masses, and the test masses 23 and 24 constitute another reflection pair of test masses, even though both reflection pairs of test masses have one test mass 23 in common.
The light beams 26 and 28 are derived from a single constant-frequency light source 36, such as a laser. A single input light beam 38 from the light source 36 is conducted through an optical fiber 40 to a beam splitter 42, and the beam splitter 42 creates the two light beams 26 and 28. Consequently, the light beams 26 and 28 in the beam arms 32 and 34 have essentially the same frequency characteristic. As an alternative to conducting the input light beam 38 through the optical fiber 40, mirrors could be used or the optical fiber 40 could be eliminated altogether by directly connecting the light source 36 to a housing 80 of the differential gradiometer 20 and directly injecting the light beam 38 into the differential gradiometer 20.
When the light beams 26 and 28 pass through the beam arms 32 and 34 and interact with both reflection pairs of freely falling test mass pairs 22, 23 and 23, 24, the increasing relative physical separation of the test masses 23 and 24 compared to the slightly-less increasing relative physical separation of the test masses 22 and 23 during simultaneous freefall, creates a changing relative phase relationship of the light beams 26 and 28 in the beam arms 32 and 34. The changed phase relationship results from the change in relative length of the beam arms 32 and 34 during simultaneous freefall of the test masses 22, 23 and 24. After passing through the beam arms 32 and 34, the light beams 26 and 28 are combined in a beam combiner 44 as an output light beam 46. Combining the light beams 26 and 28 with their relatively changing phase relationship into the single output light beam 46 creates well known optical interference fringes. The interference fringes characterize the change in physical separation of the reflection pairs of test masses 22, 23 and 23, 24 during simultaneous freefall, and that change in physical separation correlates to the differential gradient of gravity (gradient of the gradient of gravity, or second differential of gravity in the vertical direction).
An optical fiber 48 conducts the output light beam 46 to a conventional detector 50. The detector 50 generates signals which correspond to characteristics of the output light beam 46 including the interference fringes created by combining the light beams 26 and 28. A controller/processor 52 responds to signals from the detector 50 which represent the interference fringes and the timing of those fringes to determine the differential gradient of gravity directly from those interference fringes, using known interferometric analysis and processing techniques and from the known distance which separates the pairs of test masses 22, 23 and 23, 24. As an alternative to conducting the output light beam 46 through the optical fiber 48, mirrors could be used, or the optical fiber 48 could be eliminated altogether by directly connecting the detector 52 the housing 80 of the differential gradiometer 20 to directly receive the output light beam 46 from the combiner 44.
The geometry and optical components of the beam arms 32 and 34 includes four conventional corner cube retroreflectors 70a-70d positioned within the vacuum chamber 27. The retroreflectors 70a, 70b and 70c are fixed in position, and the retroreflector 70d is adjustable in position. The test masses 22 and 23 each include downward facing retroreflectors 72a and 72c, respectively, and the test masses 23 and 24 include upward facing retroreflectors 72b and 72d, respectively. The downward facing retroreflectors 72a and 72c face in the same direction that the test masses 22 and 23 freefall, and the upward facing retroreflectors 72b and 72d face in the opposite direction that the test masses 23 and 24 freefall. The retroreflectors 72a-72d are connected as a part of the test masses 22, 23 and 24.
The beam arms 32 and 34 each include five segments 74a-74e and 76a-76e, respectively, all of which extend in sequence from the beam splitter 42 to the beam combiner 44. The beam splitter 42 delivers the light beam 26 into the first segment 74a of the beam arm 32. The light beam 26 in the first segment 74a impinges upon and reflects from the downward facing retroreflector 70a into the second segment 74b of the beam arm 32. Light from the second segment 74b impinges upon reflects from the upward facing retroreflector 72d of the lower test mass 24 into the third segment 74c of the beam arm 32. Light from the third segment 74c impinges upon and reflects from the downward facing retroreflector 72c of the middle test mass 23 into the fourth segment 74d of the beam arm 32. Light from the fourth segment 74d impinges upon and reflects from the upward facing retroreflector 70b into the fifth segment 74e of the beam arm 32 leading to the beam combiner 44.
The beam splitter 42 delivers the light beam 28 into the first segment 76a of the beam arm 34. The light beam 28 in the first segment 76a impinges upon and reflects from the downward facing retroreflector 72c into the second segment 76b of the beam arm 34. Light from the second segment 74b impinges upon and reflects from the upward facing retroreflector 70b of the middle test mass 23 into the third segment 76c of the beam arm 34. Light from the third segment 76c impinges upon and reflects from the downward facing retroreflector 72a of the upper test mass 22 into the fourth segment 76d of the beam arm 34. Light from the fourth segment 76d and impinges upon and reflects from the upward facing retroreflector 70d into the fifth segment 74e of the beam arm 34 leading to the beam combiner 44.
An important aspect of the optical geometry arrangement shown in
The slightly different effects of gravity on the test masses 22, 23 and 24 during simultaneous freefall change the lengths of the beam arms 32 and 34. The relative change in the lengths of the beam arms 32 and 34 is two times the amount of relative physical separation of the test masses 22 and 23 compared to the amount of relative physical separation of the test masses 23 and 24 during simultaneous freefall. The amplification factor of two facilitates recognition of the fringes by the detector 50 and the controller/processor 52, thereby permitting more accurate calculations of the differential gradient of gravity.
This relationship of the two times change in relative length of the beam arms 32 and 34 relative to the physical separation distance of the test masses 22 and 24 is demonstrated by the following mathematical derivation.
When the lower test mass 24 falls a distance ZL, the beam arm 32 is lengthened by a distance, 2ZL, because the downward movement of the test mass 24 lengthens each beam arm segment 74b and 74c by the amount ZL, resulting in lengthening of the overall length of the beam arm 34 by the distance 2ZL. Simultaneously, when the middle test mass 23 falls a distance ZM, the beam arm 32 is shortened by a distance 2ZM, because the downward movement of the test mass 23 shortens each beam arm segment 74c and 74d by the amount ZM, resulting in lengthening of the overall length of the beam arm 32 by the distance 2ZM. The overall change in length of the beam arm 32, referred to as ΔBA32 is equal to 2ZL−2ZM, or 2(ZL−ZM).
A similar situation exists with respect to the beam arm 34. When the middle test mass 23 falls a distance ZM, the beam arm 34 is lengthened by a distance, 2ZM, because the downward movement of the test mass 23 lengthens each beam arm segment 76b and 76c by the amount ZM, resulting in lengthening of the overall length of the beam arm 34 by the distance 2ZM. Simultaneously, when the upper test mass 22 falls a distance ZU, the beam arm 34 is shortened by a distance 2ZU, because the downward movement of the test mass 22 shortens each beam arm segment 76c and 76d by the amount ZU, resulting in shortening of the overall length of the beam arm 34 by the distance 2ZU. The overall change in length of the beam arm 34, referred to as ΔBA34 is equal to 2ZM−2ZU, or 2(ZM−ZU).
When light beams 26 and 28 from the two changed-length beam arms 32 and 34 are combined by the beam combiner 44, the combined output light beam 46 contains a sinusoidal interference fringe signal whose phase is given by the difference in path length of the two beam arms 32 and 34. The difference in optical path length of the two beam arms 32 and 34, referred to herein as ΔL, is equal to the difference in change in length of the two beam arms 32 and 34, i.e. ΔBA32 and ΔBA34, respectively. Stated mathematically, ΔL=ΔBA32−ΔBA34, or ΔL=2(ZL−ZM)−2(ZM−ZU), or ΔL=2ZL−4ZM+2ZU, or. ΔL=2(ZL−2ZM+ZU).
The differential gradient of gravity is the equivalent to determining the acceleration of the change or differential in path length of the two beam arms 32 and 34. Employing this relationship in the change in path length equation derived in the previous paragraph by substituting the acceleration (a) for the distance (Z), the measured acceleration, is given by a=2(aL−aM)−2(aM−aU), where aL, aM and aU, are the accelerations of the test masses 22, 23 and 24, respectively. This equation can also be written as a=2(aL−2aM+aU). In a theoretical constant gravity field, the acceleration of all of the test masses have the same acceleration, namely g, so that the measured acceleration will be zero. This can be understood from the above equation because a=2(g−2g+g)=0.
In a different theoretical gravity field which decreases linearly as a function of the height H, above the surface of the earth, the acceleration of a freely falling object can be written as a=g−γH, where γ is referred to as the vertical gravity gradient and g is the local acceleration at the surface of the earth. If the three test masses are separated by the same distance D, the acceleration of the three objects would be given by aL=g, aM=g−Dγ, and aU=g−2Dγ, where g is acceleration of the lower test mass. Using these values, the measured acceleration of the differential path length of the two beam arms 32 and 34 is still zero, a=2[g−2(g−γD)+(g−2γD)]=0, in this theoretical gravity field. This shows that the measured acceleration is also zero in a gravity field with a theoretical linear gravity gradient.
Where the gravity field is not linear but instead decreases nonlinearly with distance above the surface of the earth, which is the actual situation on earth, the situation is represented by the equation γ=γo−ξH, where γo is a vertical gravity gradient at the surface of the earth and is the differential gradient or the gradient of the vertical gravity gradient or the second spatial derivative of gravity in the vertical direction, and H is a distance above or below the surface of the earth. Using calculus, the gravity field with a constant vertical spatial derivative of the vertical spatial derivative of gravity is written as g=go−γH−½ξH2, where go is the gravity at the surface of the earth, γ=dg/dH is the vertical gravity gradient or the first spatial derivative of gravity, and ξ=dγ/dH is the vertical gradient of the vertical gravity gradient or the second spatial derivative of gravity. This can also be written mathematically as the second vertical spatial derivative or, ξ=d2γ/dH2. Applying these formulae to calculate the accelerations of the three test masses 22, 23 and 24 with vertical separations of D, results in aL=go, aM=go−γD−½ξD2, and aU=go−2γD−2ξD2. The measured acceleration then becomes a=2[go−2(go−γD−½ξD2)aM+go−2γD−2ξD2]. After simplification, this equation becomes a=−2ξD2.
This mathematical development shows that the measured acceleration of the differential path length of the two beam arms 32 and 34 is independent of the constant part of the acceleration (or gravity, go), and also independent of the linear gradient or first spatial derivative of gravity, γ. The measured acceleration is directly proportional only to the second spatial derivative of gravity, ξ.
The equation a=−2ξD2 shows that the differential gradiometer 20 produces a sinusoidal interference fringe signal that has a phase change equal to 2 times the relative difference in the free-fall distance of the middle test mass 23 compared to each of the upper and lower freefalling test masses 22 and 24. As is discussed in the above-referenced U.S. application “Interferometric Gradiometer Apparatus and Method,” the relative difference in the freefall distances of the upper and lower test masses 22 and 24 is directly related to the gradient of gravity. Stated alternatively, the freely falling effect of the middle test mass 23 relative to the upper and lower test masses 22 and 24, creates a factor of two change in the path lengths of the test mass pairs 22, 23 and 23, 24 whenever the differential gradient of gravity is measured. This relationship is shown in
The relationship of the number of fringes 60 relative to the change in light beam path lengths caused by the moving test masses is known as an amplification factor. The differential gradiometer 20 produces an amplification factor of two in terms of the number of interference fringes 60 (
The amplification effect from the differential gradiometer 20 can also be understood generally in terms of a differential frequency shift of the light beams 26 and 28 in each of the beam arms 32 and 34 due to the well-known Doppler effect. The relative Doppler shift of light for a moving observer is given by the equation f=fo{(1+v/c)/[(1−(v/c)2]1/2}, where fo is the frequency of light in the rest frame of reference and f is the frequency in the moving frame of reference, v is a velocity of the moving observer, and c is the speed of light. For velocities that are much smaller than the speed of light, which is the case with respect to the freefalling test masses 22, 23 and 24, a first-order approximation is sufficient, so that f≅fo (1+v/c). The change in the frequency, Δf=f−fo, therefore is proportional to the ratio of the velocity of the observer to the speed of light or Δf=v/c fo.
The Doppler shift of a light beam reflecting from a moving mirror is twice this value or Δf=2 v/c fo. This can be understood because the moving mirror “sees” a Doppler shifted beam and then emits this new frequency upon reflection. However the new emitted Doppler shifted frequency is again Doppler shifted in the same manner when observed by the stationary observer, which in the case of the differential gradiometer 20, is any nonmoving portion of it. Each light beam 26 and 28 therefore experiences a Doppler shift which is related to twice the velocity of the moving mass pairs 22, 23 and 23, 24 from which the light beam reflects.
Each downward freefalling test mass shifts the light beam higher in frequency when the light beam reflects from the downward facing retroreflector and shifts the light beam lower in frequency when the light beam reflects from the upward facing retroreflector. The light beam in each beam arm reflects off of the downward facing retroreflector of one freefalling test mass and the upward facing retroreflector of the other freefalling test mass of each pair of test masses 22, 23 and 23, 24, with the net effect of giving an overall Doppler shift proportional to twice the difference in the velocities of the two falling test masses of each pair. The light beam in the other beam arm is Doppler shifted in a similar manner. When the beams are recombined, a signal with a frequency given by the difference of the frequency shift of the two light beam 32 and 34 is created. The resulting signal in the recombined output light beam is given by a Doppler shift proportional to two times the change in differential velocity of the respective pairs of falling test masses 22, 23 and 23, 24. This factor of two is the same factor of two increase in signal resolution arrived at using the description of optical path length difference in the two beam arms.
The length of the beam arms 32 and 34 is equal at one point during the simultaneous freefall of the test masses 22, 23 and 24. The change in length of the beam arms from the equality point is due only to the slightly different influence of gravity on each test mass, which causes a slightly different acceleration of each test mass, and any initial relative velocity difference imposed upon the test masses at the commencement of simultaneous freefall, as is discussed in greater detail below. If the test masses 22, 23 and 24 were subject to the same force of gravity and no initial velocity difference was imparted to any one of the test masses, the beam arms 32 and 34 would remain equal in length throughout the simultaneous freefall. When the beam arms 32 and 34 change to respectively different lengths, interference fringes are created because the unequal path lengths cause the light beam in one beam arm 32 or 34 to travel a different distance than the light beam travels in the other beam arm 34 or 32, resulting in relative phase changes which cause the interference fringes 60 (
The equal length of the beam arms 32 and 34, except for the slight variations in length caused by the slightly different influence of gravity on each test mass and any initial relative velocity difference imparted with respect to the test masses, is particularly important in eliminating the adverse effects which arise from slight frequency and phase variations in the laser light source 36. Most laser light sources 36 are subject to slight frequency and phase variations during normal operation. In addition, movement of the optical fiber 40 can also introduce frequency and phase relationships in the input light beam 38 delivered to the beam splitter 42. Even further still, if for some unanticipated reason, the beam splitter 42 should move unexpectedly relative to the input light beam 38, the light beams 26 and 28 will contain the slight frequency and phase variations. Any of these circumstances cause the light beams 26 and 28 leaving the beam splitter 42 to have slight frequency and phase variations.
When the length of the beam arms 32 and 34 is different, the phase or frequency variation of one light beam 26 or 28 passing through the different length beam arm 32 or 34 becomes shifted significantly relative to the phase or frequency variation of the other light beam 28 or 26 passing through the other beam arm 34 or 32, due to a significant difference in length of the beam arms 32 and 34. The shifted phase or frequency relationships in the two beam arms can create anomalous fringes when the light beams 26 and 28 are combined in the output light beam 46 from the beam combiner 44 because one of the light beams 26 and 28 takes longer to propogate through one of the beam arms than the other beam arm due to unequal path lengths in the beam arms 32 and 34. These anomalous fringes result from the difference in the length of the beam arms 26 and 28 and not from the differing effects of gravity influencing the freefalling test masses 22, 23 and 24. The anomalous fringes make it difficult to accurately measure the differing effects of gravity on the test masses 22, 23 and 24 and introduce a source of uncertainty or error into the measurement of the differential gradient of gravity.
Maintaining the beam arms 32 and 34 at the same length in the differential gradiometer 20, other than from the differing effects of gravity and initial relative velocity differences of the test masses, allows any phase or frequency shift created by operation of the laser light source 36 or from movement of the optical cable 40 or the beam splitter 42 to affect equally both light beams 26 and 28 and propogate through the beam arms 32 and 34 at the same time. Consequently, when the light beams 26 and 28 are recombined in the beam combiner 44, the phase and frequency shift effects on each light beam 26 and 28 are canceled by common mode rejection to avoid creating anomalous fringes. Maintaining the beam arms 32 and 34 at approximately the same length achieves this advantageous common mode rejection.
The differing effects of gravity on each of the test masses 22, 23 and 24, and an initial velocity difference imposed on the test masses 22, 23 and 24 does cause a slight difference in path length in the beam arms 32 and 34, but that amount of difference is not significant relative to the amount of phase or frequency shift created by normal operation of the laser light source 36 or from movement of the optical cable 40 or the beam splitter 42. Thus, the slight difference in length of the beam arms 32 and 34 arising from the differing effects of gravity and initial relative velocity differences, does not significantly diminish the beneficial effects of common mode rejection created by the substantially equal length beam arms 32 and 34 in the differential gradiometer 20.
The beam arms 32 and 34 are calibrated to have equal lengths by adjusting the vertical position of the retroreflector 70d in the beam arm 34, as shown in
A multiple-frequency light beam, such as a mercury band limited light beam, is used as the input light beam 38 for purposes of calibrating the length of the beam arms 32 and 34. The test masses are positioned stationarily at a position that they would occupy when the test masses commence freely falling. So long as the beam arms 32 and 34 are not equal in length, optical fringes will result in the output light beam 46 in response to the multiple-frequency input light beam. When the length of the beam arm 34 is adjusted to equal the length of the beam arm 32, by adjusting the position of the retroreflector 70d, the output light beam 46 no longer includes any optical fringes. The process flow for achieving equality in the length of the beam arms 32 and 34 is further described below in connection with
The beam arms 32 and 34 within the vacuum chamber 27 are inherently parallel to one another, despite the movement of the test masses 22 and 24. If the beam arms 32 and 34 were not parallel to one another, the non-parallel deviation of one of the beam arms would cause it to have a different length compared to the other beam arm. Such a difference in path length would cause the light beam in one beam arm to travel a different distance than the light travels in the other beam arm, resulting in relative phase changes between the light beams 26 and 28. Such resulting phase shifts from unequal beam arm lengths would create erroneous interference fringes that would lead to errors in determining the differential gradient of gravity or other characteristic of gravity being measured.
The use of a parallel surface beam splitter 42 and a parallel surface beam combiner 44 contributes to the parallelism in the beam arms 32 and 34. An inherent characteristic of the parallel surfaces of the beam splitter 42 is that the two light beams 26 and 28 are delivered in a parallel relationship. Furthermore, the two light beams 26 and 28 extend in a parallel relationship with the input light beam 38. A similar situation exists with respect to the beam combiner 44, since the beam combiner 44 is a beam splitter used for the opposite purpose. The optical characteristics of the beam combiner 44 are the same as the beam splitter 42, causing parallel light beams 26 and 28 leaving the beam arms 32 and 34 to be combined accurately in the single output beam 46 while preserving their relative phase relationship. The beam combiner 44 delivers the output signal 46 in parallel relationship to the light beams 26 and 28 delivered from the beam arms 32 and 34.
The parallel surface beam splitter 42 and the parallel surface beam combiner 44 also contribute to maintaining the previously-described substantial equality in the optical path lengths. An inherent characteristic of the parallel surface beam splitter 42 and beam combiner 44 is that the optical path length of the first light beam 26 in the beam splitter 42 added to the optical path length of the first light beam 26 in the beam combiner 44 is equal to the optical path length of the second light beam 28 in the beam splitter 42 added to the optical path length of the second light beam 28 in the beam combiner 44. As a consequence, the light beams passing through the parallel surface beam splitter 42 and beam combiner 44 retain substantial equality in optical path lengths of the beam arms 32 and 34.
The use of conventional corner cube retroreflectors 70a-70d and 72a-72d also contributes to the parallelism. Changes in direction of the light beams 26 and 28 within the vacuum chamber 27 are achieved only by the retroreflectors 70a-70d and 72a-72d. Using the retroreflectors to change the direction of the light beams ensures parallelism in the beam arms 32 and 34, thereby maintaining equal path lengths, as is understood from the following discussion of a single conventional retroreflector 75 shown in
As shown in
An incident light beam 88 enters the entry-exit surface 82 and reflects off of the reflective wall surfaces 84a-84c and then exits the retroreflector 75 through the entry-exit surface 82 as a reflected light beam 90. An optical characteristic of the retroreflector 75, which is created by the angular relationship of the reflective wall surfaces 84a-84c, is that the reflected light beam 90 always projects parallel to the incident light beam 88. This parallel relationship is maintained even if the light beam 88 does not impinge on the entry-exit surface 82 orthogonally. Unlike a mirror, the retroreflector 75 therefore reflects light back in a direction parallel to the incident light, regardless of the angle of incidence of the light beam 88 with respect to the entry-exit surface 82.
This parallel reflection quality causes the light beams in the beam arm segments 74b-74e and 76b-76e (
Conventional retroreflectors can also be of the open variety. An open retroreflector is constructed of mirrors or other high-grade reflective optical material oriented to form the reflective surfaces 84a, 84b and 84c. An open retroreflector can be used in place of each retroreflector described herein. An open retroreflector has the effect of not changing the speed of the light beam which interacts with it. A closed retroreflector changes the speed of the light beam which passes through the changed medium of the optical body of that closed retroreflector. Using open retroreflectors causes the speed of the light beam to remain constant throughout the entire beam arms 32 and 34, because the light beams do not pass through an optical body, thereby avoiding any phase or path length differences that might be created by conducting the light beams through a different medium.
The parallel relationship of the beam arms 32 and 34 is established and maintained by the beam splitter 42, the beam combiner 44 and by the retroreflectors 70a-70d and 72a-72d. This parallel relationship assures that the beam arms 32 and 34 will not deviate from parallel to create unintended path length differences. Assembling and using the differential gradiometer 20 under these circumstances is considerably easier than the tedious and often changeable nature of attempting to establish and maintain an exact angle of a reflecting mirror within a conventional gravity measuring instrument.
The optical parallelism of the beam arms 32 and 34 within the differential gradiometer 20 makes it possible to establish an exact vertical orientation of the differential gradiometer 20 during use. An exact vertical orientation of the test masses 22, 23 and 24 is essential in establishing an accurate second spatial derivative of gravity in the vertical direction, i.e. a vertical differential gradient of gravity. If the test masses 22, 23 and 24 are not exactly vertically oriented, the gradient measurement will not be completely accurate.
Because the light beams 26 and 28 in the beam arms 32 and 34 are parallel to one another in the vacuum chamber 27, due to the use of the retroreflectors 70a-70d and 72a-72d, and because output light beam 46 is parallel to the light beams 26 and 28 in the beam arms 32 and 34 due to the effect of the parallel surface beam combiner 44, a vertical orientation of the test masses 22, 23 and 24 can be established by evaluating the vertical orientation of the output light beam 46. When the output light beam 46 is vertically oriented, the test masses 22, 23 and 24 will be vertically oriented, due to the parallelism of the beam arms 32 and 34. The position of the gradiometer 20 is adjusted to achieve a precise vertical alignment of the test masses 22 and 24 as determined by the vertical projection of the output light beam 46.
Because the output light beam 46 is parallel to the light beams 26 and 28 in the beam arms 32 and 34 in the vacuum chamber 27, determining the verticality of the output light beam assures that the beam arms 32 and 34 within the vacuum chamber are also vertical. The verticality of the light beam 46 is established by disconnecting the optical fiber 48 and measuring the verticality of the projection of the light beam 46 that would otherwise pass through the optical fiber cable 48. Assuring such verticality is required to accurately measure the differential gradient of gravity in the vertical direction. Verticality can be established by reflecting the output light beam 46 from a liquid geopotential surface standard and observing the angularity of the reflected beam, as is described in detail in the above-referenced U.S. patent application Ser. No. 13/558,138.
Using the retroreflectors 72a-72d on the test masses 22, 23 and 24 also achieves advantageous improvements in avoiding the unintended spurious effects from unintended random rotation or tilting of the test masses 22, 23 and 24 during freefall. Rotation of the test masses is illustrated in
The retroreflector 75, shown in
When the retroreflector 75 is rotated about a point 94 which is not coincident with the optical center point 92, as shown in
The above described properties of retroreflectors are used to advantage in constructing the test masses 22, 23 and 24, as explained in conjunction with the middle test mass 23 shown in
The retroreflectors 72b and 72c are positioned on the test mass 23 with the entry-exit surfaces 82 facing in opposite directions and parallel with one another. The corners 86 of the retroreflectors 72a and 72b are adjacent to one another. The optical center points 92 of the retroreflectors 72b and 72c are located equidistant from a center of mass point 96 of the test mass 23. The two optical center points 92 and the center of mass point 96 are located co-linearly. The corners 86 are also located coincident with the co-linear relationship of the two optical center points 92 and the center of mass 96. In this configuration, the distance from the center of mass point 96 to the optical center point 92 of the retroreflector 72b is equal to the distance from the center of mass point 96 to the optical center point 92 of the retroreflector 72c.
The test mass 23 has a physical structure 98 which holds the two retroreflectors 72b and 72c in place. The physical structure 98 of the test mass 22 and the two retroreflectors 72b and 72c are balanced so that the center of mass point 96 of the test mass 22 is located midway between the two optical center points 92. Such balancing may be achieved by moving adjustable weights (124,
Locating the center of mass point 96 of the test mass 23 in the manner described causes the test mass 23 to rotate about the center of mass point 96 if the test mass 23 rotates while freefalling, as shown in
If the test mass 23 rotates about any point other than the center of mass point 96, then the distances over which the respective light beams in the beam arms 32 and 34 travel will not be equal. However, when the test mass 23 is freefalling, it can rotate only about its center of mass point 96, so rotation of the test mass 23 about some point other than the center of mass point 96 is not possible during freefall.
The test masses 22 and 24 each include only a single retroreflector 72a and 72d, respectively. Each test mass 22 and 24 has a physical structure (not specifically shown) which holds each retroreflector 72a and 72d in place on the respective test mass. The physical structure of the test mass 22 is balanced so that its center of mass point (not shown) is located coincident with the optical center point 92 of the retroreflector 72a. Similarly, the physical structure of the test mass 24 is balanced so that its center of mass point (not shown) is located coincident with the optical center point 92 of the retroreflector 72d. Such balancing may be achieved by moving one or more adjustable weights associated with the physical structure of the test masses 22 and 24.
Locating the center of mass points of the test masses 22 and 24 coincident with the optical center points 92 of the retroreflector 72a and 72d causes the length of the beam arms 32 and 34 to remain unaffected if one or both of the test masses 22 and 24 rotates while freefalling. Rotation about the center of mass point is also rotation about the optical center point 92 of each retroreflector 72a and 72d, and rotation about the optical center point 92 of each retroreflector 72a and 72d does not change the length of the light path through the retroreflector, as discussed above. Consequently, rotation of one or both of the test masses 22 and 24 does not affect the length of the beam arms 32 and 34, and the accuracy of measurement is not adversely affected.
An example of the physical structure 98 shown in
As shown in
The housing 100 of the test mass 22 also includes a second cup portion 114 which is defined by a cylindrical sidewall 116 and a circular top wall 118 formed on the top (as shown) of the cylindrical sidewall 116. The cylindrical sidewall 116 and the top wall 118 define an interior 120 of the second cup portion 114. The retroreflector 72a is fixed in position within the interior 120 of the second cup portion 114, with the entry-exit surface 82 of the retroreflector 72b facing upward (as shown) at or near the top wall 118. The retroreflector 72a is fixed in position within the second cup portion 114 using conventional retention techniques. At least one light beam pass-through opening 122 is formed in the top wall 118 to allow the light beams in the beam segments 76b and 76c of the beam arm 34 to impinge upon and reflect from the retroreflector 72b.
The outside diameter of the cylindrical sidewall 116 is preferably slightly smaller than the inside diameter of the cylindrical sidewall 104 to allow the bottom portion (as shown) of cylindrical sidewall 116 of the second cup portion 114 to be partially inserted into the interior 110 of the cylindrical sidewall 104 of the first cup portion 102. Threads (not shown) are formed at locations on the sidewall portions 104 and 116 to screw the two cup portions 104 and 116 firmly together as part of the housing 100.
The threaded engagement of the cylindrical side walls 104 and 116 also permits independent adjustment of the positions of the optical center points 92 of each retroreflector 72b and 72c relative to the center of mass point 96 (
The co-linear relationship of the optical center points 92 and the center of mass point 96 (
Exemplary physical structures of the upper test mass 22 and the lower test mass 24 are shown in
As shown in
The optical focal point 92 of the retroreflector 72a is located coincidentally with the center of mass 96 of the test mass 22. Similarly, the optical focal point 92 of the retroreflector 72d is located coincidentally with the center of mass 96 of the test mass 24. The balancing weights 124 achieve the coincident relationship between the optical focal points 92 and the centers of mass 96. Because the optical focal points 92 located coincidentally with the centers of mass 96 in both test masses 22 and 24, any rotation of those test masses during freefall does not change the length of the beam segments 76c, 76d and 74b, 74c, for the reason explained above that rotation of a corner cube retroreflector about its optical focal point does not change the length of the beam path. With the optical focal points 92 located coincidentally with the centers of mass 96, rotation of those test masses during freefall must occur around the center of mass 96, and therefore that rotation does not change the length of the beam arms 32 and 34.
More details of the elevator frame 30 and the support devices 31 (
The containment chambers 132, 133 and 134 are rigidly connected to each other by a pair of support tubes 136 and 138, shown in
The middle containment chamber 133 is shown in
The floor plate 154 of the upper containment chamber 132, the roof plate 150 of the lower containment chamber 134, and the roof plate 150 and the floor plate 154 of the middle containment chamber 133 include at least one light beam pass-through opening 158 which allows the light beams in the segments 74b-74d and 76b-76d of the beam arms 32 and 34 (
A flange 160 extends inward from the sidewall 146 into each containment chamber 132, 133 and 134, and an annular opening 162 extends through the flange 160. An annular sleeve 164 is inserted in the annular opening 162. The flange 160 and the annular sleeve 164 form a test mass support ring which supports each test masses 22, 23 and 24 within each containment chamber 132 and 134. The annular opening 162 and the contact support sleeve 164 receive the cylindrical sidewall 104 of the first or lower cup shaped portion 102 of the housing 100 (
To release the test masses 22, 23 and 24 to fall freely, the elevator motor 144 moves the frame structure 130 downward at an acceleration rate which is greater than the acceleration of gravity. The greater acceleration rate causes the test mass support rings formed by each flange 160 and support sleeve 164 to move downward away from the contact feet 126 on the flange 108 of each test mass (
The elevator frame structure 130 is shown in
When the test masses 22, 23 and 24 are released simultaneously to freefall, the distance between the two test mass pairs 22, 23 and 23, 24 will increase very slightly due only to the slightly greater gravity affecting the lower test mass 24 compared to the slightly lesser gravity affecting the middle test mass 23 compared to the even slightly lesser gravity effecting the upper test mass 22. The very slight increase in distance between the two freely falling test mass pairs 22, 23 and 23, 24 is difficult to detect, even with the above-described two times amplification effect of the beam arms 32 and 34. The change in distance between the two freely falling test mass pairs 22, 23 and 23, 24 might be so slight that less than one interference fringe 60 (
One way to increase the number of interference fringes is to allow the test mass pairs to fall freely for a substantial distance, thereby allowing the separation difference between the test mass pairs to increase to the point where more optical fringes are generated. This solution might be somewhat impractical for a commercial embodiment of the gradiometer, because a relatively lengthy freefall distance cannot be conveniently accommodated by the size of the device and the movement range of the elevator.
Another way to increase the number of interference fringes is by imparting a finite velocity to at least one of the test masses compared to the other two test masses at the commencement of simultaneous freefall. Imparting an initial finite velocity to one of the test masses at the instant that the other two test masses are released for freefall has the effect of changing the lengths of the beam arms 32 and 34 more than they would otherwise change if the two pairs of test masses were released simultaneously for freefall solely only under the influence of gravity. The initial finite velocity of one test mass compared to the other two test masses causes the separation distance between the test mass pairs to change to a greater extent than the change created by the difference in gravity alone acting on the test mass pairs 22, 23 and 23, 24, despite the fact that the test masses fall freely solely under the influence of gravity. The greater change in relative length of the beam arms 32 and 34 creates more interference fringes. A reasonable increase in the number of interference fringes enhances the fitted statistical recognition of those interference fringes and the ability to distinguish those interference fringes from spurious background noise.
The elevator 29, elevator frame 30 and support devices 31 may be used to impart an initial finite downward velocity to one or more of the test masses at the instant that the other one or more test mass(es) is released for freefall. The initial relative velocity difference may be imparted by using separate elevators 29, elevator frames 30 and support devices 31 (
Even though the elevator frame structure 130 rigidly connects the containment chambers 132, 133 and 134 for simultaneous movement by the elevator motor 144 (
A structural embodiment 166 of the support sleeve which creates enough flexibility to impart a relative velocity difference between the test masses is shown in
The support sleeve 166 is generally of a cylindrical configuration, and is preferably formed from a metal such as aluminum. A plurality of openings 170 are formed radially completely through the support sleeve 166 to separate solid segments 172 of the sleeve 166 by relatively narrow bands 174 of material. Each projection 168 is located between two openings 170, and two openings are located at opposite ends of each solid segment 172. The projections 168 extend outward from the support sleeve 166 between adjacent openings 170. Foot rests 176 extend upward from the center of each solid segment 172. Each foot rest 176 includes a notch 178 which is adapted to receive one contact foot 126 extending from the flange 108 of the test mass 22. The notches 178 of the foot rests 176 are located at the same circumferential positions where the contact feet 126 are located around the flange 108 of the test mass 22.
When the test mass 22 rests on the support sleeve 166 as shown in
When the elevator frame structure 130 is accelerated downward, the test mass 22 remains supported on the foot rests 176 while the narrow bands 174 begin rebounding from the downward flexed position and move the solid segments 172 upwardly while the test mass 22 remains supported from the foot rests 176. The downward acceleration of the frame structure 130 increases until the narrow bands 174 are no longer deflected downwardly, and at that point the test mass 22 is released for freefall solely under the influence of gravity. In this manner, the spring characteristics of narrow bands 174 delay the time when the test mass 22 is released for freefall. Under certain circumstances, the downward deflection of the narrow bands 174 may cause them to rebound slightly into an upper deflection, in which case the narrow bands 174 may impart an slight, momentary artificial upward acceleration to the test mass 22 which causes an even greater time delay before the test mass commences freefall solely under the influence of gravity. Of course, the effect of delaying the commencement of freefall solely under the influence of gravity allows the other test mass to achieve a finite velocity before the delayed test mass commences downward freefall solely under the influence of gravity. The increased separation distance between the test masses results in an increased the number of fringes generated, and the increased number of fringes facilitates fitted statistical detection of the vertical gradient of gravity.
Another technique to generate numerous fringes is to employ two different-frequency input light beams 38a and 38b from two different constant-frequency light sources, such as the laser light sources 210 and 212, in a differential gradiometer 20a as shown in
The respectively different frequencies of the light beams 26 (38a) and 28 (38b) in the two beam arms 32 and 34 will inherently create fringes 60 (
An embodiment 20b of a differential gradiometer which uses mirrors is shown in
The half mirror 221a replaces the beam splitter 42 (
The single sided full mirror 225b receives the light beam 28 passed through the half mirror 221a and reflects the light beam 28 to the double sided full mirror 223b. Light from the full mirror 223b is reflected to the retroreflector 72a of the upper test mass 22. The beam arm 34 is then reflected from the retroreflector 72a to the retroreflector 72b of the middle test mass 23, and then from the retroreflector 72b to the other side of the double sided full mirror 223b. The light reflected from the full mirror 223b then passes to the half mirror 221b where the light beam 28 is reflected from the half mirror 221b and combines with the light beam 26 passing through the half mirror 221b to form the output light beam 46.
The use of the half mirrors 221a and 221b and the double sided full mirrors 223a and 223b and the single sided full mirrors 225a and 225b require precision positioning to achieve the parallel relationship of the segments of the light beams 26 and 28, because the mirrors do not inherently direct the incident and reflected beams in a parallel relationship as do the retroreflectors 70a-70d (
The embodiments of the differential gradiometers 20, 20a and 20b described in connection with
In the differential gradiometer 20c shown in
Various aspects of the process flow involved in measuring the differential gradient of gravity in the vertical direction and the use of the differential gradiometers described above are illustrated in
An exemplary process flow 224 for establishing equal length of the beam arms 32 and 34 is illustrated in
The output signal 46 is then detected by the detector 50 and processed by the controller/processor 52 (
An exemplary process flow 240 for determining the differential gradient of gravity using a single constant-frequency input light beam is illustrated in
An exemplary process flow 260 for determining the differential gradient of gravity using two different-frequency, constant-frequency input light beams 38a and 38b (
One of the benefits of the present invention is that the differential gradient of gravity is determined and made available very quickly after the termination of the simultaneous freefall of the test masses. The interference fringe characteristics define the differential gradient of gravity directly, and thereby avoid the necessity to measure two gradient of gravity values, subtract those gravity gradient values from one another, and then divide the difference by the separation distance to obtain the differential gradient of gravity. The interference fringe characteristics in the output light beam 46 directly define the differential gradient of gravity, thereby achieving an immediate value of the differential gradient of gravity.
Differential gradient of gravity information is especially useful for detecting subterranean anomolies near the surface 280 of the earth 282, as illustrated in
The differential gradiometers described herein may be moved across the surface 280 of the earth 284 in an airplane 288 or other vehicle. As the airplane 288 moves above and across the surface 280 of the earth, the differential gradiometer passes over the subterranean anomalies 284 and 286, as understood from
The advantageous common mode rejection characteristics of the differential gradiometer allows it to be employed successfully and accurately in a vibration-prone environment such as in the airplane 288 (
Many significant improvements result from the present invention, as previously discussed and reiterated below. The high level of effective common mode rejection cancels or ameliorates most external noise influences. The common mode rejection results in substantial part because beam arms 32 and 34 (
Balancing the test masses 22, 23 and 24 with their centers of mass relative to the optical center points of their retroreflectors preserves the relative length relationship of the beam arms 32 and 34, despite rotation of the test masses that might occur during freefall. Rotation of the upper and lower test masses 22 and 24 does not change the optical path of both beam arms 32 and 34, and the rotation of the middle test mass 23 causes equal length changes in both beam arms 32 and 34. The rotation of the test masses during freefall no longer constitutes an additional source of anomalous interference fringes which adversely influence the measurement of the gravity gradient.
The equal length characteristics of the beam arms 32 and 34 are facilitated by the use of the parallel path optical elements 44, 46, 70a-70d and 72a-72d (
The amplification factor of two, which is achieved by reflecting both light beams in both beam arms 32 and 34 from both pairs of test masses 22, 23 and 23, 24 represents an improvement in resolution. The practical benefit is that the test masses do not require as much distance to freefall to achieve adequate resolution. A differential gradiometer with the higher amplification factor can be made smaller and more compact than a differential gradiometer having a lower amplification factor.
Common mode rejection is also achieved in the input light beam 38 and the output light beam 46. Any frequency and phase shifts from the single laser light source 36 are present equally in the light beams 26 and 28 conducted in the beam arms 32 and 34, since the light beams 26 and 28 are derived from the single input light beam 38 (
Imparting an initial relative velocity difference to the two freely falling test masses facilitates the creation of more interference fringes which are useful in improving the measurement of the differential gradient of gravity. The common mode rejection capability permits the initial relative velocity difference to be imparted to the test masses in such a way as not to introduce anomalies arising from imparting the initial relative velocity difference.
Many other advantages and improvements will become apparent upon fully appreciating the many aspects of the present invention. Presently preferred embodiments of the present invention and many of its improvements have been described with a degree of particularity. This description is preferred examples of implementing the invention, and is not necessarily intended to limit the scope of the invention. The scope of the invention is defined by the scope of the following claims.
This invention is continuation in part of an invention described in U.S. patent application Ser. No. 13/558,138, titled “Interferometric Gradiometer Apparatus and Method,” filed Jul. 25, 2012. This invention is also a continuation in part of an invention described in U.S. patent application Ser. No. 13/564,548 titled “Test Mass and Method for Interferometric Gravity Characteristic Measurement,” filed Aug. 1, 2012. Both of these applications were filed by the inventors hereof, and both applications have been assigned to the assignee hereof. The subject matter of these U.S. patent applications is incorporated herein by this reference.
| Number | Date | Country | |
|---|---|---|---|
| Parent | 13558138 | Jul 2012 | US |
| Child | 13586114 | US | |
| Parent | 13564548 | Aug 2012 | US |
| Child | 13558138 | US |
