CN108897057B - Full-tensor gravity gradient measurement method based on optical suspension and gravity gradiometer - Google Patents

Full-tensor gravity gradient measurement method based on optical suspension and gravity gradiometer Download PDF

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CN108897057B
CN108897057B CN201810377078.3A CN201810377078A CN108897057B CN 108897057 B CN108897057 B CN 108897057B CN 201810377078 A CN201810377078 A CN 201810377078A CN 108897057 B CN108897057 B CN 108897057B
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CN108897057A (en
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缪立军
牟家鹏
庞斌
黄腾超
胡慧珠
舒晓武
刘承
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Zhejiang University ZJU
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Abstract

The invention discloses a full-tensor gravity gradient measurement method based on optical power suspension and a gravity gradiometer. The method comprises the steps of respectively arranging three microsphere optical suspension triaxial sensing units at three points of a three-dimensional space, wherein the three microsphere optical suspension triaxial sensing units are not collinear, respectively measuring the gravity acceleration at the three points through the microsphere optical suspension triaxial sensing units, and then obtaining the total tensor of the gravity gradient by utilizing a difference principle. The microsphere optical force suspension triaxial sensing unit comprises a sensing microsphere suspension module and a sensing microsphere displacement detection module, wherein the sensing microsphere suspension module realizes the suspension of sensing microspheres by utilizing an optical force effect, the sensing microsphere displacement detection module realizes the triaxial displacement detection of the sensing microspheres by utilizing a light intensity balance detection principle, and then the triaxial gravity acceleration is calculated by utilizing the rigidity of the optical force suspension unit. The invention can realize the high-sensitivity measurement of the full tensor of the gravity gradient and effectively reduce the integration difficulty of the full-tensor gravity gradiometer.

Description

Full-tensor gravity gradient measurement method based on optical suspension and gravity gradiometer
Technical Field
The invention relates to a testing device, in particular to a full-tensor gravity gradient measuring method based on optical suspension and a gravity gradiometer.
Background
The gravity field is a geophysical basic field reflecting the internal material structure and its transition of the earth, and the gravity gradient represents the change rate of gravity acceleration in a certain direction in unit distance and has the unit of s-2(the unit is E, 1E-10-9s-2) The gravity anomaly caused by density change in the earth is reflected, the resolution ratio of the gravity anomaly is higher than that of gravity measurement, and the gravity anomaly detection method is more suitable for a motion platform. Based on these advantages, gravity gradient measurement has extremely important application in the fields of geodetic surveying, resource exploration, gravity navigation and the like.
Gravity gradient is gravity acceleration vector
Figure GDA0001765488330000011
In a Cartesian coordinate systemDerivatives in the three directions x, y, z, which form the gravity gradient tensor matrix, as shown in equation (1):
Figure GDA0001765488330000012
the gravity gradient tensor matrix T is a symmetric matrix satisfying Txy=Tyx,Tyz=Tzy,Tzx=TxzAnd the three axial gravity gradients satisfy Txx+Tyy+TzzThe gravity gradient therefore has only 5 independent components. The full tensor gradiometer is an instrument capable of measuring all 5 independent gravity gradient tensors simultaneously, and the research thereof is deeply valued by scientific researchers at home and abroad.
At present, a full-tensor gravity gradiometer mature internationally is a rotating accelerometer gravity gradiometer, the basic principle of which is shown in fig. 1, 4 accelerometers are symmetrically distributed on a disc, the sensitive directions of the accelerometers are along the tangential direction of the disc, the disc is made to rotate at a certain angular velocity, output signals of the accelerometers a 1-a 4 are collected, signals of the acceleration a1 are added to signals of the accelerometer a2, signals of the accelerometer a3 are added to signals of the accelerometer a4, and then the two signals are subtracted, so that 3 signals containing gravity gradient information are obtained. The method adopts three mutually vertical turntables to install 12 accelerometers so that the turntables rotate at the same angular speed, adopts the same signal acquisition method to obtain 9 signals containing gravity gradient elements, and can solve 5 independent gravity gradient tensors by a mathematical method.
The gravity gradiometer with the rotary accelerometer can measure the full tensor of the gravity gradient, but the gravity gradiometer needs the accelerometer with extremely high measurement precision, and simultaneously has the errors of the installation direction of the accelerometer, the nonlinear error of the accelerometer, the inconsistent scale factors among the accelerometers, the errors generated by the non-strict orthogonality of all sensitive axes and the like.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a full-tensor gravity gradient measurement method based on optical suspension and a gravity gradiometer.
A full tensor gravity gradient measurement method based on optical suspension is characterized in that three microsphere optical suspension triaxial sensing units are respectively arranged at three points of a three-dimensional space and are not collinear, the gravity acceleration at the three points is respectively measured through the microsphere optical suspension triaxial sensing units, and then the full tensor of the gravity gradient is obtained by utilizing a difference principle.
The method adopts three microsphere optical power suspension triaxial sensing units with the same structure, and the space coordinates are respectively (d, 0, 0) on an X axis, (0, d, 0) on a Y axis and (0, 0, d) on a Z axis; the gravity acceleration (g) at (d, 0, 0) is measured by the microsphere optical force suspension triaxial sensing unit1x,g1y,g1z) The acceleration of gravity (g) at (0, d, 0) is measured2x,g2y,g2z) The acceleration of gravity (g) at (0, 0, d) is measured3x,g3y,g3z),
The gravity gradient in the corresponding direction is obtained by utilizing the difference principle, and the calculation formula is as follows:
Figure GDA0001765488330000021
wherein, TxxIs gxRate of change in direction along the x-axis, TyyIs gyRate of change in the y-axis direction, TzzIs gzRate of change along the z-axis; t isxyIs gyRate of change in direction along the x-axis, TyxIs gxRate of change in the y-axis direction, TxzIs gzRate of change in direction along the x-axis, TzxIs gxRate of change in direction along the x-axis, TyzIs gzRate of change in the y-axis direction, TzyIs gyRate of change along the z-axis.
The microsphere optical force suspension triaxial sensing unit comprises a sensing microsphere suspension module and a sensing microsphere displacement detection module, wherein the sensing microsphere suspension module realizes the suspension of sensing microspheres by utilizing an optical force effect, the sensing microsphere displacement detection module realizes the triaxial displacement detection of the sensing microspheres by utilizing a light intensity balance detection principle, and then the triaxial gravity acceleration is calculated by utilizing the rigidity of the optical force suspension unit.
A full-tensor gravity gradiometer based on optical suspension by adopting the method comprises three microsphere optical suspension three-axis sensitive units with the same structure, wherein the space coordinates are respectively (d, 0, 0) on an X axis, (0, d, 0) on a Y axis and (0, 0, d) on a Z axis;
the microsphere optical power suspension triaxial sensing unit arranged on the Z axis (0, 0, D) comprises a suspension beam laser, an acousto-optic modulator, a first beam splitter, a first focusing lens, an optical power meter, a dichroic mirror, a first reflecting mirror, a second focusing lens, a detection beam laser, a second reflecting mirror, sensing microspheres, a first band-pass filter, a second beam splitter, a first D-shaped mirror, a third reflecting mirror and a Z-axis balance detector;
the suspension beam laser emits horizontal suspension laser which passes through the acousto-optic modulator and is divided into horizontal suspension laser beams and vertical upward power reference laser beams by the first beam splitter, wherein the power reference laser beams enter the optical power meter after passing through the first focusing lens, then the acousto-optic modulator is modulated according to a power test result, the power of the suspension laser beams is kept stable, the suspension laser beams respectively pass through the dichroic mirror and the first reflecting mirror and are transmitted vertically upwards, and then the suspension laser beams pass through the second focusing lens and interact with the sensitive microspheres to enable the sensitive microspheres to be suspended;
the detection beam laser respectively emits vertical downward detection light and vertical upward detection light, wherein the vertical downward detection light is reflected by the dichroic mirror and then is transmitted with the suspension light beam in a common path;
the dichroic mirror is selected according to the wavelengths of the suspension light beams and the detection light beams, so that the suspension light beams can be transmitted through the dichroic mirror, and the detection light beams are reflected to be transmitted to the right horizontally;
the vertical upward detection light is changed into horizontal rightward transmission after passing through the second reflecting mirror, passes through the sensitive microsphere region and then is transmitted through the first band-pass filter, then passes through the second beam splitter and then is changed into horizontal rightward Z-axis detection light beams and vertical upward X-axis detection light paths, wherein the Z-axis detection light beams respectively enter two detection points of the Z-axis balance detector after being reflected by the first D-shaped mirror and the third reflecting mirror, then the displacement of the sensitive microspheres in the Z-axis direction is obtained through photoelectric conversion and signal difference, and then the displacement is brought into the rigidity in the Z-axis direction, so that the corresponding gravity acceleration can be obtained.
The invention has the beneficial effects that:
the invention uses three microsphere optical suspension triaxial sensing units which are respectively arranged at three points of a three-dimensional space to measure the triaxial components of the gravity acceleration at the three points, and then uses the difference principle to obtain the gravity gradient full tensor. The optical suspension triaxial sensing unit of the microsphere can reach 10-14The N/mum-magnitude rigidity and the gravity acceleration measurement sensitivity can reach 100μm/g, so that the high-sensitivity measurement of the gravity gradient can be realized through difference, and meanwhile, the three-axis measurement of the gravity acceleration can be realized through a single microsphere optical force suspension three-axis sensing unit, so that the integration difficulty of a full-tension gravity gradiometer can be effectively reduced.
Drawings
FIG. 1 is a schematic diagram of a prior art rotary accelerometer gravity gradiometer;
FIG. 2 is a schematic diagram of force analysis of a sensitive microsphere in a Gaussian beam; (a) a scattering force generation principle, (b) a gradient force generation principle;
FIG. 3 is a schematic diagram of the gradient force generation principle of a sensitive microsphere in a Gaussian beam; (a) a convergent light gradient force generation principle, (b) a divergent light gradient force generation principle;
FIG. 4 is a schematic structural diagram of a microsphere optical suspension triaxial sensing unit in the present invention;
the system comprises a suspended light beam laser 1, an acousto-optic modulator 2, a first beam splitter 3, a first focusing lens 4, an optical power meter 5, a dichroic mirror 6, a first reflecting mirror 7, a second focusing lens 8, a detection light beam laser 9, a second reflecting mirror 10, sensitive microspheres 11, a first band-pass filter 12, a second beam splitter 13, a first D-shaped mirror 14, a third reflecting mirror 15, a third focusing lens 16, a fourth focusing lens 17, a Z-axis balance detector 18, a second D-shaped mirror 19, a fourth reflecting mirror 20, a fifth focusing lens 21, a sixth focusing lens 22, an X-axis balance detector 23, a second band-pass filter 24, a third D-shaped mirror 25, a fifth reflecting mirror 26, a seventh focusing lens 27, an eighth focusing lens 28, a Y-axis balance detector 29, a suspended light beam 100, a modulated suspended light beam 101, a power reference light beam 102, a vertically downward detection light beam 103, a vertical downward detection light beam 103, a light beam splitter 3, a detection system and a detector, wherein, A vertical upward probe beam 104, a Z-axis probe beam 105, an X-axis probe beam 106, a Z-axis D-type specular beam 107, a Z-axis balance reference beam 108, an X-axis D-type specular beam 109, an X-axis balance reference beam 110, a Y-axis probe beam 111, a Y-axis D-type specular beam 112, and a Y-axis balance reference beam 113;
FIG. 5 is a schematic diagram of the full tensor gravity gradiometer principle of the invention based on optical force levitation;
the X-axis direction microsphere optomechanical suspension triaxial sensing unit A1, the Y-axis direction microsphere optomechanical suspension triaxial sensing unit A2 and the Z-axis direction microsphere optomechanical suspension triaxial sensing unit A3.
Detailed Description
In order that the principles, objects, aspects and advantages of the present invention will become more apparent, the present invention will be further described in detail with reference to the accompanying drawings.
The light beam is a group of photon flow with mass and momentum, when the light irradiates the surface of an object and interacts with the object, the momentum change of the photon generates force action on the irradiated object, and the light beam can be divided into two parts: scattering forces due to reflection and gradient forces due to refraction.
As shown in FIG. 2(a), the Gaussian beam is irradiated onto the microsphere for reflection, and the incident beam
Figure GDA0001765488330000041
After being reflected by the small ball, the light beam becomes a reflected light beam
Figure GDA0001765488330000042
A momentum difference is created and the photons transfer this momentum to the microsphere. The microspheres are subjected to a scattering force
Figure GDA0001765488330000043
Assuming that the ball is centered in the Gaussian beam, it is subjected to the same amount of force on the other side
Figure GDA0001765488330000044
The resultant of these two forces is along the direction of light transmission, i.e., because the scattering forces experienced by the reflective microspheres in a gaussian beam are always along the direction of light transmission.
As shown in fig. 2(b), the principle of refraction generating gradient force can be analyzed using the above method, except that the direction of the gradient force is independent of the direction of light transmission. Assuming that the intensity of the light on the left side is greater than the intensity on the right side, the particles on the left side are subjected to a gradient force
Figure GDA0001765488330000051
Will be greater than the gradient force to which the particle on the right side is subjected
Figure GDA0001765488330000052
I.e. the resultant force will be directed towards the left side of the particle.
To better explain the direction of the resultant of the gradient forces, the following two cases are introduced for comparison, as shown in fig. 3, from which it can be derived that for convergent light the direction of the gradient force to which the beads are subjected is along the direction of transport of the light, and for divergent light the direction of the gradient force to which the beads are subjected is opposite to the direction of transport of the light. In combination with the above two cases, it follows that the direction of the gradient force is always directed to where the light in the beam is powerful.
Based on the analysis, the interaction between the Gaussian beam and the microsphere can form an optical potential well, and the particles are stably bound in the center of the potential well, namely, the suspension of the microsphere is realized.
Based on the optical suspension effect, the invention provides a full tensor gravity gradient measurement method based on optical suspension.
The microsphere optical force suspension triaxial sensing unit comprises a sensing microsphere suspension module and a sensing microsphere displacement detection module, wherein the sensing microsphere suspension module realizes the suspension of sensing microspheres by utilizing an optical force effect, the sensing microsphere displacement detection module realizes the triaxial displacement detection of the sensing microspheres by utilizing a light intensity balance detection principle, and then the triaxial gravity acceleration is calculated by utilizing the rigidity of the optical force suspension unit.
The structure of the microsphere optical force suspension triaxial sensing unit is shown in figure 4. The whole sensitive unit comprises a suspended beam laser 1, an acousto-optic modulator 2, a first beam splitter 3, a first focusing lens 4, an optical power meter 5, a dichroic mirror 6, a first reflecting mirror 7, a second focusing lens 8, a detection beam laser 9, a second reflecting mirror 10, a sensitive microsphere 11, a first band-pass filter 12, a second beam splitter 13, a first D-shaped mirror 14, a third reflecting mirror 15, a third focusing lens 16, a fourth focusing lens 17, a Z-axis balance detector 18, a second D-shaped mirror 19, a fourth reflecting mirror 20, a fifth focusing lens 21, a sixth focusing lens 22, an X-axis balance detector 23, a second band-pass filter 24, a third D-shaped mirror 25, a fifth reflecting mirror 26, a seventh focusing lens 27, an eighth focusing lens 28 and a Y-axis balance detector 29.
The suspension beam laser 1 emits a horizontal rightward suspension beam 100 (with a typical wavelength value of 1064nm) which passes through the acousto-optic modulator 2, and then is divided into a horizontal rightward modulated suspension beam 101 and a vertical upward power reference beam 102 by the first beam splitter 3, wherein the power reference beam 102 passes through the first focusing lens 4 and then enters the optical power meter 5, and then the acousto-optic modulator 2 is modulated according to a power test result, so that the power of the modulated suspension beam 101 is kept stable. The suspended light beam 101 vertically transmits upwards after passing through the dichroic mirror 6 and the first reflecting mirror 7 respectively, and then passes through the second focusing lens 8 to interact with the sensitive microspheres 11, so that the suspended light beam is suspended and then reaches the second band-pass filter 24 to be blocked.
The detection beam laser 9 emits a vertical downward detection beam 103 and a vertical upward detection beam 104 (with a typical wavelength of 532nm), respectively, wherein the vertical downward detection beam 103 is reflected by the dichroic mirror 6 and then transmitted in a common path with the modulated suspension beam 101, passes through the sensitive microsphere region and then reaches the second band-pass filter 24, is transmitted by the second band-pass filter 24 and then becomes a Y-axis detection beam 111, wherein a part of the light is reflected by the third D-shaped mirror 25 and then becomes a Y-axis D-shaped mirror reflection beam 112, and is horizontally transmitted to the left, and is converged at one detection point of the Y-axis balance detector 29 by the seventh focusing lens 27, and another part of the light of the Y-axis detection beam 111 is reflected by the fifth mirror 26 and then becomes a Y-axis balance reference beam 113, and is horizontally transmitted to the left, and is converged at another detection point of the Y-axis balance detector 29 by the eighth focusing lens 28.
In the test process, when the acceleration of gravity in the Y-axis direction borne by the sensitive microsphere 11 increases, the microsphere moves in the positive Y-axis direction, which causes the increase of the light intensity of the Y-axis D-type mirror reflected light beam 112 and the decrease of the light intensity of the Y-axis balanced reference light beam 113, and then the displacement of the sensitive microsphere 11 in the Y-axis direction can be obtained by performing photoelectric conversion and signal differentiation through the Y-axis balanced detector 29, and then the acceleration of gravity in the Y-axis direction at the sensitive microsphere 11 can be obtained by bringing the displacement into the rigidity in the Y-axis direction.
Dichroic mirror 6 is selected based on the wavelengths of the levitating light beam and the probe light beam to allow the modulated levitating light beam 101 to transmit therethrough and the vertically downward probe light beam 103 to reflect as a horizontal rightward transmission.
The second band-pass filter 24 is selected according to the wavelengths of the floating light and the detection light, and transmits the Y-axis detection light 111, blocks the floating light, and isolates the influence of the floating light on the detection of the displacement of the microsphere.
The vertical upward detection light 104 passes through the second reflecting mirror 10 to become horizontal and transmitted to the right, passes through the sensitive microsphere region and then is transmitted through the first band-pass filter 12, passes through the second beam splitter 13 and then becomes horizontal rightward Z-axis detection light beams 105 and vertical upward X-axis detection light beams 106, wherein part of the Z-axis detection light beams 105 is reflected by the first D-type mirror 14 to become Z-axis D-type reflection light beams 107 and transmitted vertically downward, and is converged at one detection point of the Z-axis balance detector 18 through the third focusing lens 16, and the other part of the Z-axis detection light beams 105 is reflected by the third reflecting mirror 15 to become Z-axis balance reference light beams 108 and transmitted vertically downward, and is converged at the other detection point of the Z-axis balance detector 18 through the fourth focusing lens 17.
In the test process, when the gravity acceleration in the Z-axis direction borne by the sensitive microsphere 11 increases, the pellet moves in the positive direction of the Z-axis, which causes the light intensity of the Z-axis D-type mirror reflected light beam 107 to decrease and the light intensity of the Z-axis balance reference light beam 108 to increase, and then the displacement of the sensitive microsphere 11 in the Z-axis direction can be obtained by performing photoelectric conversion and signal difference through the Z-axis balance detector 18, and then the gravity acceleration in the Z-axis direction at the sensitive microsphere 11 can be obtained by bringing the rigidity in the Z-axis direction.
Part of the light of the vertical upward X-axis detection beam 106 is reflected by the second D-type mirror 19 to become an X-axis D-type reflected beam 109, and then horizontally transmitted to the right, and then converged to one detection point of the X-axis balanced detector 23 through the fifth focusing lens 21, and another part of the light of the X-axis detection beam 106 is reflected by the fourth mirror 20 to become an X-axis balanced reference beam 110, and then horizontally transmitted to the right, and finally converged to another detection point of the X-axis balanced detector 23 through the sixth focusing lens 22.
In the test process, when the gravity acceleration in the X-axis direction received by the sensitive microsphere 11 increases, the microsphere moves in the positive direction of the X-axis, which causes the light intensity of the X-axis D-type mirror reflected light beam 109 to decrease and the light intensity of the X-axis balanced reference light beam 110 to increase, and then the light intensity is subjected to photoelectric conversion and signal differentiation by the X-axis balanced detector 23, so that the displacement of the sensitive microsphere 11 in the X-axis direction can be obtained, and then the rigidity in the X-axis direction is brought in, so that the gravity acceleration in the X-axis direction at the position of the sensitive microsphere.
The first band-pass filter 12 is selected according to the wavelengths of the floating light and the detection light, and transmits the Z-axis detection beam 105 and the X-axis detection beam 106 therethrough, so as to block the floating light and isolate the influence of the floating light on the detection of the displacement of the microsphere.
As shown in fig. 5, the full-tensor gravity gradiometer based on optical suspension of the invention comprises an X-axis direction microsphere optical suspension triaxial sensing unit a1 with spatial coordinates (d, 0, 0), a Y-axis direction microsphere optical suspension triaxial sensing unit a2 with spatial coordinates (0, d, 0), and a Z-axis direction microsphere optical suspension triaxial sensing unit A3 with spatial coordinates (0, 0, d).
Wherein the X-axis direction microsphere optical suspension triaxial sensing unit A1 can measure the gravity acceleration (g) at (d, 0, 0)1x,g1y,g1z) The gravity acceleration (g) of the corresponding test point can be measured by the corresponding microsphere optomechanical suspension triaxial sensitive unit A2 in the Y-axis direction and the microsphere optomechanical suspension triaxial sensitive unit A3 in the Z-axis direction2x,g2y,g2z) And (g)3x,g3y,g3z) The gravity gradient in the corresponding direction can be obtained by utilizing the difference principle, and the calculation formula is as follows:
Figure GDA0001765488330000071
and (3) carrying out differential calculation according to the formula (2) and three microsphere optical suspension triaxial sensitive units which are arranged at a certain space interval to realize the full tensor test of the gravity gradient.

Claims (1)

1. A full tensor gravity gradient measurement method based on optical suspension is characterized in that three microsphere optical suspension triaxial sensing units are respectively arranged at three points of a three-dimensional space and are not collinear, the gravity acceleration at the three points is respectively measured through the microsphere optical suspension triaxial sensing units, and then the full tensor of the gravity gradient is obtained by utilizing a difference principle;
three microsphere optical power suspension triaxial sensing units with the same structure are adopted, and the space coordinates are (d, 0, 0) on an X axis, (0, d, 0) on a Y axis and (0, 0, d) on a Z axis respectively;
the gravity acceleration (g) at (d, 0, 0) is measured by the microsphere optical force suspension triaxial sensing unit1x,g1y,g1z),
The acceleration of gravity (g) at (0, d, 0) is measured2x,g2y,g2z),
The acceleration of gravity (g) at (0, 0, d) is measured3x,g3y,g3z),
The gravity gradient in the corresponding direction is obtained by utilizing the difference principle, and the calculation formula is as follows:
Figure FDA0002386732360000011
wherein, TxxIs gxRate of change in direction along the x-axis, TyyIs gyRate of change in the y-axis direction, TzzIs gzRate of change along the z-axis; t isxyIs gyRate of change in direction along the x-axis, TyxIs gxRate of change in the y-axis direction, TxzIs gzRate of change in direction along the x-axis, TzxIs gxRate of change in direction along the x-axis, TyzIs gzRate of change in the y-axis direction, TzyIs gyRate of change along the z-axis;
the microsphere optical-force suspension triaxial sensing unit comprises a sensitive microsphere suspension module and a sensitive microsphere displacement detection module, wherein the sensitive microsphere suspension module
The light force effect is utilized to realize the suspension of the sensitive microspheres, the sensitive microsphere displacement detection module utilizes the light intensity balance detection principle to realize the triaxial displacement detection of the sensitive microspheres, and then the triaxial gravity acceleration is calculated by utilizing the rigidity of the light force suspension unit.
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