阅读说明：本技术 一种航空重力梯度仪实时重力梯度解调方法及装置 (Real-time gravity gradient demodulation method and device for aviation gravity gradiometer ) 是由 钱学武 赵立业 于 2020-06-30 设计创作，主要内容包括：本发明公开了一种航空重力梯度仪实时重力梯度解调方法及装置,属于精密测量领域。方法包括：首先对四只加速度计输出信号进行信号调理和滤波；然后A/D转换器根据角度信息转换器发出的同步脉冲信号对滤波后的重力梯度模拟信号进行A/D转换,得到重力梯度数字信号；接下来利用参考信号源对重力梯度数字信号进行相位角解调,得到解调相位角；最后利用解调相位角、角度信息和参考信号源对重力梯度数字序列进行实时重力梯度解调,得到具有时空信息的重力梯度数据。使用本发明提供的航空重力梯度仪实时重力梯度解调方法,能够进一步提高重力梯度测量精度,操作简单方便,同时可为后续的离线处理和地质分析提供丰富的数据材料。(The invention discloses a real-time gravity gradient demodulation method and device for an aviation gravity gradiometer, and belongs to the field of precision measurement. The method comprises the following steps: firstly, signal conditioning and filtering are carried out on output signals of four accelerometers; then the A/D converter performs A/D conversion on the filtered gravity gradient analog signal according to the synchronous pulse signal sent by the angle information converter to obtain a gravity gradient digital signal; then, phase angle demodulation is carried out on the gravity gradient digital signal by using a reference signal source to obtain a demodulation phase angle; and finally, carrying out real-time gravity gradient demodulation on the gravity gradient digital sequence by using the demodulation phase angle, the angle information and the reference signal source to obtain gravity gradient data with space-time information. The real-time gravity gradient demodulation method of the aviation gravity gradiometer provided by the invention can further improve the measurement precision of the gravity gradient, is simple and convenient to operate, and can provide abundant data materials for subsequent off-line processing and geological analysis.)

1. A real-time gravity gradient demodulation method for an aviation gravity gradiometer is characterized by comprising the following steps:

performing signal conditioning and filtering on signals output by the four accelerometers to obtain gravity gradient analog signals;

the A/D converter performs A/D conversion on the filtered gravity gradient analog signal according to the synchronous pulse signal sent by the angle information converter to obtain a gravity gradient digital signal;

carrying out phase angle demodulation on the gravity gradient digital signal by using a reference signal source to obtain a demodulated phase angle;

and carrying out real-time gravity gradient demodulation on the gravity gradient digital sequence by using the demodulation phase angle, the angle information output by the angle information converter and a reference signal source to obtain gravity gradient data with space-time information.

2. The real-time gravity gradient demodulation method of the aviation gravity gradiometer according to claim 1, wherein the gravity gradient digital signal expression form obtained by the a/D converter is:

E_out(k)＝2K_IKR{(_yy-_xx)sin2[ωΔt(k-1)-α]+2_xycos2[ωΔt(k-1)-α]}

in the formula, K is data sequence index, K is system signal amplification gain, Δ t is sampling time, and K is_IIs an accelerometer scale factor, R is the disk radius, ω is the disk rotation angular frequency, α is the gravity gradient demodulation phase angle, E_out(k) Is a digital signal at the (k-1) th time Δ t, Г_xxIs the spatial derivative of the acceleration of gravity component on the x-axis in the direction of the x-axis, Г_yyIs the spatial derivative of the acceleration of gravity component on the y-axis in the y-direction, (Г)_yy-Г_xx) Is a gravity gradient Г_yyAnd Г_xxDifference of Г_xyIs the spatial derivative of the gravity acceleration component on the x (y) axis in the direction of the y (x) axis, the coordinate system OXYZ of the gravity gradiometer on which the x axis and the y axis are located is the northeast geographic coordinate system, and the origin O is the measurement center of the gravity gradiometer.

3. The airborne gravity gradiometer real-time gravity gradient demodulation method of claim 1 wherein the phase angle demodulation of the gravity gradient digital signal using the reference signal source comprises:

sends out digital sine signal S_s(k, i) and a digital cosine signal S_c(k, i) as a reference signal;

the phase angle demodulation is carried out on the output signal of the A/D converter by using the reference signal, and the calculation formula is as follows:

in the formula (I), the compound is shown in the specification,

4. The airborne gravity gradiometer real-time gravity gradient demodulation method of claim 3, further comprising: demodulating phase angle of obtained gravity gradient

5. The aviation gravity gradiometer real-time gravity gradient demodulation method of claim 2, wherein the gravity gradient demodulation expression is:

in the formula, p is the index of the sequence of the number of turns of the disk rotation at the current moment, M is the total number of turns of the disk rotation, GPS is the position information provided by the GPS, and theta_p,kThe disc angular position information is output in real time by the angle information converter.

6. The utility model provides a real-time gravity gradient demodulating equipment of aviation gravity gradiometer which characterized in that includes:

the signal conditioning module is used for conditioning and filtering signals output by the four accelerometers to obtain gravity gradient analog signals;

the A/D conversion module is used for carrying out A/D conversion on the filtered gravity gradient analog signal according to the synchronous pulse signal sent by the angle information module to obtain a gravity gradient digital signal;

the angle information module is used for sending out a synchronous pulse signal and outputting the disc angle information in real time;

the phase angle demodulation module is used for demodulating the phase angle of the gravity gradient digital signal by using a reference signal source to obtain a demodulated phase angle; and

and the gravity gradient demodulation module is used for carrying out real-time gravity gradient demodulation on the gravity gradient digital sequence by utilizing the demodulation phase angle, the angle information and the reference signal source to obtain the gravity gradient data with the space-time information.

7. The real-time gravity gradient demodulation device of the aviation gravity gradiometer according to claim 6, wherein the gravity gradient digital signal expression form obtained by the A/D conversion module is as follows:

E_out(k)＝2K_IKR{(_yy-_xx)sin2[ωΔt(k-1)-α]+2_xycos2[ωΔt(k-1)-α]}

in the formula, K is data sequence index, K is system signal amplification gain, Δ t is sampling time, and K is_IIs an accelerometer scale factor, R is the disk radius, ω is the disk rotation angular frequency, α is the gravity gradient demodulation phase angle, E_out(k) Is a digital signal at the (k-1) th time Δ t, Г_xxIs the spatial derivative of the acceleration of gravity component on the x-axis in the direction of the x-axis, Г_yyIs the spatial derivative of the acceleration of gravity component on the y-axis in the y-direction, (Г)_yy-Г_xx) Is a gravity gradient Г_yyAnd Г_xxDifference of Г_xyIs the spatial derivative of the gravity acceleration component on the x (y) axis in the direction of the y (x) axis, the coordinate system OXYZ of the gravity gradiometer on which the x axis and the y axis are located is the northeast geographic coordinate system, and the origin O is the measurement center of the gravity gradiometer.

8. The airborne gravity gradiometer real-time gravity gradient demodulation apparatus of claim 6 wherein the phase angle demodulation module comprises:

a reference signal generating unit for generating a digital sinusoidal signal S_s(k, i) and a digital cosine signal S_c(k, i) as a reference signal;

the calculating unit is used for demodulating the phase angle of the output signal of the A/D conversion module according to the reference signal, and the calculating formula is as follows:

in the formula (I), the compound is shown in the specification,

9. The airborne gravity gradiometer real-time gravity gradient demodulation apparatus of claim 8 wherein the phase angle demodulation module further comprises: an optimization unit for demodulating the phase angle of the obtained gravity gradientAnd ζ_qAnd combining, filtering the combined data through a zero-phase low-pass filter, and averaging the processed phase angles to obtain a final gravity gradient demodulation phase angle α.

10. The real-time gravity gradient demodulation device of the aviation gravity gradiometer according to claim 7, wherein the expression of the gravity gradient demodulation module for real-time gravity gradient demodulation is as follows:

in the formula, p is the index of the sequence of the number of turns of the disk rotation at the current moment, M is the total number of turns of the disk rotation, GPS is the position information provided by the GPS, and theta_p,kThe disc angular position information is output in real time by the angle information converter.

Technical Field

The invention belongs to the technical field of precision measurement, and particularly relates to a real-time gravity gradient demodulation method and device for an aviation gravity gradiometer.

Background

The high-precision aviation gravity gradient measurement technology has important significance for the research in the fields of space science, earth science, geological science, energy exploration, inertial navigation and the like. At present, the gravity gradiometers mainly include a rotary accelerometer gravity gradiometer, a superconducting gravity gradiometer, a cold atom gravity gradiometer, an electrostatic gravity gradiometer, a gravity gradiometer based on a micro-machining (MEMS) technology, and the like, wherein the rotary accelerometer gravity gradiometer is the only currently commercially available gravity gradiometer which is successfully used on an onboard/shipborne moving base. Airborne gravity gradient measurements are favored for their economy, high efficiency, and high resolution that is unique to small-scale geological targets.

The gravity gradiometer of the rotary accelerometer is a high-precision measuring instrument, the stability of electronic elements, the electromagnetic compatibility problem of electronic circuits, the working performance of a sensor, the stability of a rotating mechanism, the temperature control performance and other factors can cause serious influence on the measurement precision of the gravity gradiometer, and the factors can cause the output signal of the gravity gradiometer to contain various noises, thereby reducing the measurement precision. In the prior art, a lot of work is done to improve the measurement accuracy of the gravity gradient, and some achievements are obtained, for example, patent CN108873093B discloses a self-gradient compensation method of an aviation gravity gradiometer, which improves the measurement accuracy of the gravity gradient by compensating the self-gradient caused by attitude change in the operation process of a carrier; the patent CN110471123A discloses a method for diagnosing and processing data of a gravity gradiometer of a rotating accelerometer, which improves the measurement accuracy by reasonably diagnosing and processing the data of the gravity gradient; patent CN109212619B discloses a device and a method for compensating linear motion errors of a gravity gradiometer of a rotary accelerometer, patent CN109212629B discloses a device and a method for compensating angular motion errors of a gravity gradiometer of a rotary accelerometer, patent CN109212620B discloses a device and a method for compensating errors of a gravity gradiometer of a rotary accelerometer of a movable base, and patent CN110068876A discloses a method for compensating motion errors of an aviation gravity gradiometer based on carrier self-vibration, wherein the error compensation methods are used for researching angular motion errors, linear motion errors, self-gradients and vertical motion errors in the working process of the gravity gradiometer and compensating the angular motion errors, the linear motion errors, the self-gradients and the vertical motion errors by a specific method, so that the measurement performance of a machine is improved. However, besides the above influence factors, the accurate determination of the demodulation phase angle of the gravity gradient is also an important influence factor, which directly influences the gravity gradient measurement performance. The error of the demodulation phase angle mainly comes from the aspects of the stability of a rotating mechanism, the control stability of a motor, circuit noise, transmission delay caused by signal processing and the like, but no relevant documents are published or published for the error compensation of the demodulation phase angle of the aeronautical gravity gradiometer at present.

Disclosure of Invention

The purpose of the invention is as follows: in order to overcome the defects of the prior art, the invention provides the method and the device for demodulating the real-time gravity gradient of the aviation gravity gradiometer, which have the advantages of simple operation, convenient implementation and strong practicability, solves the problem of the reduction of the gravity gradient measurement performance caused by inaccurate gravity gradient demodulation phase angle, and can provide important application reference for high-precision aviation gravity gradient measurement.

The technical scheme is as follows: in order to achieve the purpose, the invention adopts the following technical scheme:

in a first aspect, a real-time gravity gradient demodulation method for an aviation gravity gradiometer is provided, which comprises the following steps:

performing signal conditioning and filtering on signals output by the four accelerometers to obtain gravity gradient analog signals;

the A/D converter performs A/D conversion on the filtered gravity gradient analog signal according to the synchronous pulse signal sent by the angle information converter to obtain a gravity gradient digital signal;

carrying out phase angle demodulation on the gravity gradient digital signal by using a reference signal source to obtain a demodulated phase angle;

and carrying out real-time gravity gradient demodulation on the gravity gradient digital sequence by using the demodulation phase angle, the angle information output by the angle information converter and a reference signal source to obtain gravity gradient data with space-time information.

Wherein the gravity gradient digital signal expression form is as follows:

E_out(k)＝2K_IKR{(_yy-_xx)sin2[ωΔt(k-1)-α]+2_xycos2[ωΔt(k-1)-α]}

in the formula, K is data sequence index, K is system signal amplification gain, Δ t is sampling time, and K is_IIs an accelerometer scale factor, R is the disk radius, ω is the disk rotation angular frequency, α is the gravity gradient demodulation phase angle, E_out(k) Is a digital signal at the (k-1) th time Δ t, Г_xxIs the spatial derivative of the acceleration of gravity component on the x-axis in the direction of the x-axis, Г_yyIs the spatial derivative of the acceleration of gravity component on the y-axis in the y-direction, (Г)_yy-Г_xx) Is a gravity gradient Г_yyAnd Г_xxDifference of Г_xyIs the spatial derivative of the gravity acceleration component on the x (y) axis in the direction of the y (x) axis, the coordinate system OXYZ of the gravity gradiometer on which the x axis and the y axis are located is the northeast geographic coordinate system, and the origin O is the measurement center of the gravity gradiometer.

Further, the phase angle demodulation of the gravity gradient digital signal by using the reference signal source comprises:

sends out digital sine signal S_s(k, i) and a digital cosine signal S_c(k, i) as a reference signal;

the phase angle demodulation is carried out on the output signal of the A/D converter by using the reference signal, and the calculation formula is as follows:

in the formula (I), the compound is shown in the specification,

ζ_ithe correction angles of the initial phase angles of the sine signal reference source and the cosine signal reference source at the ith time are respectively, the right side | max of the equation represents the initial phase angle of the sine signal reference source and the cosine signal reference source corresponding to the searched maximum value, N is the pulse number output by the angle information converter when the disc rotates once,ζ_qand respectively demodulating phase angles for the gravity gradient obtained for the q-th time.

As a preferred embodiment, a gravity gradient demodulation phase angle is obtainedAnd ζ_qThen, toAnd ζ_qAnd combining, filtering the combined data through a zero-phase low-pass filter, and averaging the processed phase angles to obtain a final gravity gradient demodulation phase angle α.

The gravity gradient demodulation expression is as follows:

in the formula, p is the index of the sequence of the number of turns of the disk rotation at the current moment, M is the total number of turns of the disk rotation, GPS is the position information provided by the GPS, and theta_p,kThe disc angular position information is output in real time by the angle information converter.

In a second aspect, a real-time gravity gradient demodulation device for an aviation gravity gradiometer is provided, which includes:

the signal conditioning module is used for conditioning and filtering signals output by the four accelerometers to obtain gravity gradient analog signals;

the A/D conversion module is used for carrying out A/D conversion on the filtered gravity gradient analog signal according to the synchronous pulse signal sent by the angle information module to obtain a gravity gradient digital signal;

the angle information module is used for sending out a synchronous pulse signal and outputting the disc angle information in real time;

the phase angle demodulation module is used for demodulating the phase angle of the gravity gradient digital signal by using a reference signal source to obtain a demodulated phase angle; and

and the gravity gradient demodulation module is used for carrying out real-time gravity gradient demodulation on the gravity gradient digital sequence by utilizing the demodulation phase angle, the angle information and the reference signal source to obtain the gravity gradient data with the space-time information.

Has the advantages that: the invention provides a processing method for real-time gravity gradient demodulation of an aviation gravity gradiometer for the first time from an actual measurement system, can realize gravity gradient demodulation phase angle compensation and high-precision gravity gradient demodulation, improves the gravity gradient measurement precision, has the characteristics of simple and convenient operation, convenient implementation, strong applicability and the like, and has important reference value for improving the aviation gravity gradient measurement performance of a movable base.

Drawings

FIG. 1 is a schematic diagram of the working principle of the real-time gravity gradient demodulation method of the aviation gravity gradiometer of the invention;

FIG. 2 shows gravity gradient information (Г) before and after phase compensation for gravity gradient demodulation according to an embodiment of the invention_yy-Г_xx) A comparative waveform plot;

FIG. 3 is a diagram illustrating gravity gradient information Г before and after phase compensation for gravity gradient demodulation according to an embodiment of the invention_xyComparative waveform diagrams.

Detailed Description

The technical scheme of the invention is further explained by combining the attached drawings.

Fig. 1 is a schematic diagram of a method for demodulating a real-time gravity gradient of an airborne gravity gradiometer according to the present invention, and is described with reference to fig. 1, the method comprising the following steps:

1) the gravity gradiometer is placed on a stable platform, the measurement center of the gravity gradiometer is taken as an original point O, and the northeast geographic coordinate system is taken as the coordinate system of the gravity gradiometer and is marked as oxyz;

2) the output signals of the four accelerometers are processed by a signal conditioning and filtering circuit to obtain an analog signal E_out(t) the angle information converter outputs the synchronization pulse signal to the A/D converter, and the A/D converter outputs the analog signal E_out(t) A/D conversion is carried out to obtain a digital signal E at the (k-1) th time delta t_out(k) The expression is as follows:

E_out(k)＝2K_IKR{(_yy-_xx)sin2[ωΔt(k-1)-α]+2_xycos2[ωΔt(k-1)-α]}

in the formula, K is data sequence index, K is system signal amplification gain, Δ t is sampling time, and K is_IFor accelerometer scale factors, R is the disk radius, ω is the disk rotation angular frequency, α is the gravity gradient demodulation phase angle, Г_xxIs the spatial derivative of the acceleration of gravity component on the x-axis in the direction of the x-axis, Г_yyAs the component of gravitational acceleration in the y-axisSpatial derivative in the y-axis direction, (Г)_yy-Г_xx) Is a gravity gradient Г_yyAnd Г_xxDifference of Г_xyIs the spatial derivative of the gravitational acceleration component in the x (y) axis in the y (x) axis direction;

3) solving the gravity gradient demodulation phase angle by adopting the following formula:

in the formula (I), the compound is shown in the specification,ζ_ithe correction angles of the initial phase angles of the sine signal reference source and the cosine signal reference source at the ith time are respectively, N is the pulse number output by the angle information converter when the disc rotates once,

ζ_qdemodulation of the phase angle, S, for the q-th gravity gradient obtained_s(k,i)、S_c(k, i) are reference signal source digital sine and cosine signals respectively, which are sent out by DSP simulation and can be expressed by the following expressions:

4) demodulating phase angle of obtained gravity gradientAnd ζ_qCombining in a way of connecting in sequence to obtain

ζ₁,ζ₂,...,ζ_qThen, filtering the combined data through a zero-phase low-pass filter, and finally performing mean processing on the processed phase angle to obtain a gravity gradient demodulation phase angle α in real time;

5) angle information converter on grating angle encoder outputs disc angle position in real timeTheta is_p,kUsing angular position information theta_p,kCarrying out real-time gravity gradient demodulation on the gravity gradient digital signal to obtain gravity gradient data with space-time information, wherein a demodulation expression is as follows:

in the formula, p is the index of the sequence of the number of revolutions of the disk at the current moment, M is the total number of revolutions of the disk, and GPS is the position information provided by the GPS.

Based on the implementation steps of the aviation gravity gradiometer real-time gravity gradient demodulation method, the effectiveness of the method is verified through an example. Setting the base line distance of the disc to be 1m, the scale factor of the accelerometer to be 32mA/g and the gravity acceleration to be 9.81m/s²The rotation period of the disc is 20s, the sampling rate is 2Hz, and the accelerometer A is arranged at the initial moment₁The included angle between the X axis and the X axis is 0 degree, the side length of the environment object is 0.3m of a cube, and the density is 18200kg/m³The distance between the center of the environmental object and the center of the GGI is 0.72m, the induced azimuth angle is 0 degrees, the gravity gradient output signal is processed, the demodulation phase angle of the gravity gradient is calculated to be-50.29 degrees, the delay is mainly caused by a signal processing channel, and the gravity gradient component (Г) caused by the environmental object can be obtained through calculation_yy-Г_xx) And Г_xyThe theoretical values of (A) are-335 Eu and 0Eu, respectively, if the gravity gradient demodulation phase angle processing is not performed, if the initial phase angle of 0 degree is adopted as the gravity gradient demodulation phase angle, the gravity gradient component is demodulated (Г)_yy-Г_xx) And Г_xy61.89Eu and 164.62Eu respectively, and the error between the theoretical gradient value and the theoretical gradient value reaches several hundred Eu, therefore, the demodulation of the original gravity gradient data can generate a very large measurement error, the aviation gravity gradient measurement can not be carried out, if the demodulation phase angle calculated by the method provided by the invention is used as the gravity gradient demodulation initial phase angle to demodulate the gravity gradient signal, the gravity gradient component is obtained by demodulation (Г)_yy-Г_xx) And Г_xyBetween-335.0085 Eu and 0.00055Eu, respectively, and the theoretical gradient valueThe error is less than 0.01Eu, the aviation gravity gradient measurement requirement can be met, and the gradient information before and after the gravity gradient demodulation phase compensation is compared as shown in figures 2 and 3.

According to another embodiment of the present invention, there is provided an aviation gravity gradiometer real-time gravity gradient demodulation apparatus, including:

the signal conditioning module is used for conditioning and filtering signals output by the four accelerometers to obtain a gravity gradient analog signal, and optionally, the signal conditioning module adopts a signal conditioning and filtering circuit;

the A/D conversion module is used for carrying out A/D conversion on the filtered gravity gradient analog signal according to the synchronous pulse signal sent by the angle information module to obtain a gravity gradient digital signal, and optionally, the A/D conversion module adopts an A/D converter;

the angle information module is used for sending out a synchronous pulse signal and outputting disc angle information in real time, and optionally, the angle information module adopts an angle information converter on a grating angle encoder;

the phase angle demodulation module is used for demodulating the phase angle of the gravity gradient digital signal by using a reference signal source to obtain a demodulated phase angle; and

and the gravity gradient demodulation module is used for carrying out real-time gravity gradient demodulation on the gravity gradient digital sequence by utilizing the demodulation phase angle, the angle information and the reference signal source to obtain the gravity gradient data with the space-time information.

Optionally, the phase angle demodulation module and the gravity gradient demodulation module employ a DSP.

Specifically, the expression form of the gravity gradient digital signal obtained by the a/D converter is:

E_out(k)＝2K_IKR{(_yy-_xx)sin2[ωΔt(k-1)-α]+2_xycos2[ωΔt(k-1)-α]}

in the formula, K is data sequence index, K is system signal amplification gain, Δ t is sampling time, and K is_IIs an accelerometer scale factor, R is the disk radius, ω is the disk rotation angular frequency, α is the gravity gradient demodulation phase angle, E_out(k) Is a digital signal at the (k-1) th time delta t,Г_xxis the spatial derivative of the acceleration of gravity component on the x-axis in the direction of the x-axis, Г_yyIs the spatial derivative of the acceleration of gravity component on the y-axis in the y-direction, (Г)_yy-Г_xx) Is a gravity gradient Г_yyAnd Г_xxDifference of Г_xyIs the spatial derivative of the gravitational acceleration component in the x (y) axis in the direction of the y (x) axis.

The coordinate system of the x axis and the y axis is a gravity gradiometer coordinate system OXYZ, the coordinate system adopts a northeast geographic coordinate system, and the origin O is a gravity gradiometer measurement center.

The phase angle demodulation module includes: a reference signal generating unit for generating a digital sinusoidal signal S_s(k, i) and a digital cosine signal S_c(k, i) as a reference signal source; the reference signal expression is:

and the calculation unit is used for demodulating the phase angle of the gravity gradient digital signal by using a reference signal source to obtain a demodulated phase angle, and the calculation solving formula is as follows:

in the formula (I), the compound is shown in the specification,ζ_ithe correction angles of the initial phase angles of the sine signal reference source and the cosine signal reference source at the ith time are respectively, the right side | max of the equation represents the initial phase angle of the sine signal reference source and the cosine signal reference source corresponding to the maximum value, the initial phase angle is continuously changed until the maximum amplitude is obtained, N is the pulse number output by the angle information converter when the disc rotates for each circle,

ζ_qand respectively demodulating phase angles for the gravity gradient obtained for the q-th time.

As a preferred embodimentThe phase angle demodulation module also comprises an optimization unit for demodulating the phase angle of the obtained gravity gradientAnd ζ_qAre combined and sequentially connected to obtainζ₁,ζ₂,...,ζ_qThe combined data is filtered by a zero-phase low-pass filter, and the processed phase angles are averaged to obtain a final gravity gradient demodulation phase angle α.

The expression of the gravity gradient demodulation module for carrying out real-time gravity gradient demodulation is as follows:

in the formula, p is the index of the sequence of the number of turns of the disk rotation at the current moment, M is the total number of turns of the disk rotation, GPS is the position information provided by the GPS, and theta_p,kThe disk angular position information is output in real time by the angular information converter on the grating angular encoder.

The above examples are only preferred embodiments of the present invention, it should be noted that: it will be apparent to those skilled in the art that various modifications and equivalents can be made without departing from the spirit of the invention, and it is intended that all such modifications and equivalents fall within the scope of the invention as defined in the claims.