GB2558310A

GB2558310A - Methods and systems for radar detection of rotational motion

Info

Publication number: GB2558310A
Application number: GB1622442.0A
Authority: GB
Inventors: Narbudowicz Adam; Dallmann Thomas; J Amman Max; Heberling Dirk
Original assignee: Rheinisch Westlische Technische Hochschuke RWTH; Dublin Institute of Technology
Current assignee: Rheinisch Westlische Technische Hochschuke RWTH; Dublin Institute of Technology
Priority date: 2016-12-30
Filing date: 2016-12-30
Publication date: 2018-07-11
Also published as: EP3563171A1; GB201622442D0; WO2018122396A1

Abstract

A method and apparatus of measuring the rotation of a target, wherein the target manipulates the phase of an incident polarised radar signal depending on its orientation, comprising steps of: transmitting an elliptically or linearly polarised signal towards the target, receiving a scattered signal from the target, measuring a phase change of the received signal over time, calculating a change in orientation of said target. The transmitted elliptically polarised radar signal may be circularly polarised. The transmit and receive antennae may be co-located. The target may be provided on a body such that the rotation of the body may be measured. A second polarised signal may be transmitted having the same polarisation state as the first but a different frequency. The received signals from the dual frequency interrogation may be used to isolate the frequency independent manipulation of the phase on scattering from the frequency dependent due to the distance traversed by the wave.

Description

(56) Documents Cited:

US 4728897 A1 (71) Applicant(s):

Dublin Institute of Technology (Incorporated in Ireland)

143-149 Rathmines Road, Rathmines D6, Dublin 6, Ireland (58) Field of Search:

INT CL G01S

Other: WPI, EPODOC, TXTA

Rheinisch-Westfalische Technische Hochschule (RWTH) Aachen

Templergraben 55, 52062 Aachen, Germany (72) Inventor(s):

Adam Narbudowicz Thomas Dallmann Max J. Amman Dirk Heberling (74) Agent and/or Address for Service:

FRKelly

Mount Charles, BELFAST, Northern Ireland, BT7 1NZ, United Kingdom (54) Title of the Invention: Methods and systems for radar detection of rotational motion

Abstract Title: Measuring the rotation of a target which manipulates the phase depending on its orientation when scattering a polarised radar signal.

(57) A method and apparatus of measuring the rotation of a target, wherein the target manipulates the phase of an incident polarised radar signal depending on its orientation, comprising steps of: transmitting an elliptically or linearly polarised signal towards the target, receiving a scattered signal from the target, measuring a phase change of the received signal overtime, calculating a change in orientation of said target. The transmitted elliptically polarised radar signal may be circularly polarised. The transmit and receive antennae may be co-located. The target may be provided on a body such that the rotation of the body may be measured. A second polarised signal may be transmitted having the same polarisation state as the first but a different frequency. The received signals from the dual frequency interrogation may be used to isolate the frequency independent manipulation of the phase on scattering from the frequency dependent due to the distance traversed by the wave.

This print incorporates corrections made under Section 117(1) of the Patents Act 1977.

1/7

Fig. 1B

2/7

CW radar

3/7

4/7

Voltage (V)

Time (ns)

5/7

6/7

Fig. 7

136

7/7

Fig. 9

Methods and systems for radar detection of rotational motion

Technical Field

This invention relates to radar systems, and radar detection methods, which can be used to detect rotational motion.

Background Art

The detection of rotation and measurement of rotation speed is an important area of metrology. Applications include detection of helicopters and drones, monitoring the operation of turbines, and diagnostics and monitoring of devices with movable components including for example engines and flow meters. Radar can be a useful tool because it is a contactless, remote measurement method which can be used to measure the rotation of bodies that are invisible or hidden. Using radar to measure the rotation of internal components of a system can also permit measurement in cases where the system does not report such rotation speeds, and where it is not practical or cost-effective to install rotation sensors in the system itself.

Measuring the rotation of a body using radar presents different challenges depending on the axis of rotation and its orientation to the radar source and detector.

Referring to Fig. 1A, a simple system is shown in which a radar system 10 having an antenna 12 for both transmitting and receiving signals is disposed a distance from a body 14, which in this case is a flat, thin cylinder. A line 16 between the antenna and the body can be used to define a coordinate reference system of orthogonal axes. The axes are arbitrarily labelled x, y and z.

In Fig. 1A the body 14 is indicated to be spinning around the central axis of symmetry of the cylinder, which is coincident with the line 14 and lies parallel to the z axis. Referring additionally to Fig. IB, which shows the same system viewed side-on, it can be seen that if the body 14 is a sufficient distance from the antenna 12, the radar wavefront 18 reaching the body is planar or nearly so in the x-y plane.

Therefore, the situation illustrated can be described as one in which the axis of rotation (denoted by the line 16) is normal or perpendicular to the wavefront 18. Clearly, it would also be possible for the cylindrical body 14 to be rotating about a second orthogonal vertical axis (as viewed in Fib. IB), in the manner of a spinning coin, so that the axis of rotation is parallel to the y-axis, or for it to be rotating about a third orthogonal axis perpendicular to the plane of the drawing (and thus normal to both the vertical axis and the line 16, and parallel to the x-axis).

Both the second and third axes could then be described as defining axes of rotation parallel to the plane or pseudo-plane of the wavefront 18.

In reality a body may not be regular like the cylinder, and the rotation may not be simply about a single one of these axes. The rotation may be more complex and it may have components of rotation relative to each of the x, y and z-axes. The axis of rotation may not pass through the body at all. However, for the purposes of this description one may note that any rotation of a solid body can be decomposed into angular components, one of which is the component of rotation about an axis normal to the wavefront, and it is this rotational component which is most challenging to measure without using complex equipment.

For rotation about an axis or rotation that is parallel to the plane of the wavefront, the body will often (depending on its shape and volumetric composition) produce a Doppler effect. Even a spherical body can be provided with a radar reflective (or absorptive) marker whose motion will be detectable using the Doppler effect using any continuous wave (CW) radar.

However, for the component of rotation of a body about the axis normal to the wavefront, even if provided with a marker, no rotation can be detected using a standard CW radar, assuming that the radar the second and is a sufficient distance from the target so as to be unable to spatially track the marker as it rotates. It is this rotation with which the present invention is primarily concerned.

The invention is intended to address one or more ofthe problems associated with existing radar measurement systems and methods for measuring a component of rotation about an axis normal to a radar wavefront.

Disclosure ofthe Invention

There is provided a method of measuring rotation of a target, comprising the steps of:

a) transmitting an elliptically polarised radar signal towards a target, wherein the target manipulates the phase of the radar signal depending on its orientation around an axis defined by the direction of propagation of the transmitted radar signal;

b) receiving a scattered signal from the target using an elliptically polarized receive antenna, wherein the scattered signal is linearly or elliptically polarised;

c) measuring a phase change of the received signal over time;

d) calculating a change in orientation of said target relative to said axis, said change in orientation being determined as an angle φ which is proportional to the phase change of the signal, the phase change being calculated according to the formula:

V_rx = ^md^kre^j2c^ [Eq. i] where V_rx is the voltage received by the receive antenna; m is a normalisation factor; j is the imaginary unit; k is the wavenumber of the radar signal; r is the round trip distance from the transmit antenna to the target and back to the receive antenna; and φ is the phase change in the received signal.

Preferably, the transmitted, elliptically polarised, radar signal is circularly polarised. The inventors have found that if an appropriately shaped target is illuminated by an elliptically polarized transmit signal, the scattered (i.e. reflected) waves are either linearly polarized or are elliptically polarized with a phase of the signal exhibiting strongly linear dependency on the orientation of the object with respect to axis normal to the wavefront.

An appropriately shaped target is a target which manipulates the phase and possibly the magnitude of the radar signal depending on its orientation around the axis defined by the direction of propagation of the transmitted radar signal. A simple case would be an elongated conductive body like a copper bar, which is disposed (for example) vertically, or using the notation of Fig. IB parallel to the y-axis. Such a body will reflect or scatter the radiation most strongly when the electric field of the incident radar signal is aligned vertically, and most weakly when the field is aligned horizontally. In the ideal case, for illumination with circularly polarized wave the reflected signal reaches a maximum at the points in the incident wave's period when the field is vertically aligned and falls to zero during the points in the incident wave's period when the field is vertically aligned. Therefore, the reflected signal would be vertically linearly polarized. (The term reflect, as used herein, refers to the scattering that occurs in the direction of the observer.)

Preferably, the target has a scattering matrix defined by:

’dip = me'^a

COS²0 cos φ sin φ cos<f> sin </> sin²</>

[Eq. 2] wherein a is a function of the wavenumber k and round trip distance r, and is preferably the product kr.

Advantageously, the method can further include the step of providing said target on a body such that the rotation of the body is measurable by the rotation of the target. Thus, for example, in the case of a body not having the desired scattering characteristics, a reflector having the desired scattering matrix can be provided on or in any rotating body to provide such a target.

On a circularly polarized receive antenna, one observes a voltage that varies sinusoidally and is of the form A cos(cot + φ) where A is the amplitude, ω is the frequency (assuming a single frequency signal) and φ is the phase shift.

Now if the target is rotated clockwise by e.g. 90 degrees, then the overall amplitude A of reflection throughout a complete period will be unchanged, but the reflection maxima and minima will be shifted to a point that is later or earlier in the cycle by 180 degrees, thus constituting a phase shift of the signal.

More generally, a shift of phase in the received signal pattern will signify a rotational shift in the body, by half the angle. An engine part, which is metallic and elongated in one direction when viewed in the plane of the wavefront, which rotates at a speed of 600 r.p.m. (or 10 rotations per second) will be detectable as a phase shift of 20 x 2π rad/s. A dielectric disk, as seen in Fig. 1A and IB, will be observable if it is fitted with an elongated metallic marker lying along a diameter.

In general it is also possible to reverse the situation, where the target is illuminated by linearly polarized wave and the target reflects back a circularly polarized wave, with a suitable target being used.

Accordingly, there is also provided a method of measuring rotation of a target, comprising the steps of:

a) transmitting a linearly polarised radar signal towards a target, wherein the target manipulates the phase of the radar signal depending on its orientation around an axis defined by the direction of propagation of the transmitted radar signal;

b) receiving a scattered signal from the target using a linearly polarized receive antenna, wherein the scattered signal is circularly or elliptically polarised;

c) measuring a phase change of the received signal over time;

V_rx = ±^me^jkre^j2^ [Eq. 3]

Where V_rx is the voltage received by the receive antenna; m is a normalisation factor; j is the imaginary unit; k is the wavenumber of the radar signal; r is the round trip distance from the transmit antenna to the target and back to the receive antenna; and φ is the phase change in the received signal.

Preferably, in this case, the received radar signal is circularly polarised.

Preferably, said target has a scattering matrix defined by:

S_Mx = me^]a j t^Ecl· ⁴1 wherein a is a function of the wavenumber k, round trip distance r, and phase φ.

More preferably, said target has a scattering matrix defined by:

Shix = me^]kre^]2(t) + . [Eq. 5]

One preferred embodiment of a target is a generally planar helical reflector.

A further preferred embodiment of target takes the form of one or more pairs of dihedral reflectors, wherein in each pair a first dihedral reflector comprises first and second reflective planes meeting at a first seam, the first seam defining a first seam axis, and the second dihedral reflector comprises third and fourth reflective planes meeting at a second seam, the second seam defining a second seam axis which is rotated relative to the first seam axis about a rotation axis orthogonal to the first and second seam axes by an angle Θ, and wherein the first and second seams are offset from each other along the direction of the rotation axis, by an amount equal to λ(Μ ± 1/8) where λ is the wavelength of the radar signal with which the target is to be used, and M is an integer. In a preferred embodiment M is zero, so that the offset is plus or minus one-eighth of a wavelength.

Preferably, where the target comprises more than one pair of dihedral reflectors, the first seam axis of each pair is parallel to the first seam axis of each other pair.

Further preferably, the second seam axis of each pair is rotated relative to the first seam axis by the same angle Θ.

Preferably, the angle Θ is between 40 and 50 degrees, most preferably 45 degrees.

In a particularly preferred embodiment, the target comprises two pairs of reflectors disposed alongside one another, and the target is rotationally symmetrical about a central axis, such that the first reflectors are diagonally opposite one another across the central axis and the second reflectors are diagonally opposite one another across the central axis.

Preferably, in this embodiment, when viewed from the direction of the central axis, each of the four reflectors presents a square shape, and the target is of the form of a 2x2 square centred on the central axis.

Further preferably, the second seam axis of each pair is co-linear and meets at the central axis.

In a preferred embodiment, the transmitted signal is generated by a transmit antenna that is colocated with the receive antenna.

If the transmit antenna is separated from the receive antenna with an angular separation between the lines connecting the target to the respective antennae, then the rotation will generally be measured with respect to the axis defined by the receive wavefront. However in such cases the target can be modified with e.g. a reflective tag that reflects more energy in the direction of the receive antenna, rather than simply directly back to the transmit antenna.

If the rotating body is moving towards or away from the transmitter or receiver, the situation becomes more complex. There will be a phase change associated with the target movement the e^jkr term in Eq. 1 - and a phase change associated with any rotation of the target.

The method may further comprise the steps of:

transmitting a second signal, having the same polarization state (elliptical or linear) as in step (a) (i.e. in the case where the first transmitted signal is circularly/elliptically polarized, the second signal is likewise circularly/elliptically polarized, and where the first signal is linearly polarized, the second signal is likewise linearly polarized), but of a different frequency to the signal in step (a);

receiving a second scattered signal from the target at that different frequency, as in step (b), measuring a second phase change for the second received signal over time; and determining from the first and second phase changes a frequency independent phase change component attributable to the change in φ, and a frequency dependent phase change component attributable to the change in kr, and thereby determining both the change in distance and the change in orientation.

Preferably, the transmitted radar signal is a continuous wave signal.

In another aspect there is provided a radar system for measuring rotation of a target, comprising:

a) an elliptically polarised transmit antenna configured to transmit an elliptically polarized radar signal towards a target, wherein the target manipulates the phase of the radar signal depending on its orientation around an axis defined by the direction of propagation of the transmitted radar signal;

b) an elliptically polarized receive antenna configured to receive a scattered signal from the target, wherein the scattered signal is linearly or elliptically polarised;

c) signal processing means for measuring a phase change of the received signal over time;

d) a processor programmed to calculate a change in orientation of said target relative to said axis, said change in orientation being determined as an angle φ which is proportional to the phase change of the signal, the phase change being calculated according to the formula:

V_rx = ^me^Jkr [Eq. 1] where V_rx is the voltage received by the receive antenna; m is a normalisation factor; j is the imaginary unit; k is the wavenumber of the radar signal; r is the round trip distance from the transmit antenna to the target and back to the receive antenna; and φ is the phase change in the received signal.

The system may advantageously also include said target, wherein said target has a scattering matrix defined by:

’dtp = me'^a

COS²0 cos φ sin φ cos<fi sin φ sin²</>

[Eq- 2] wherein a is a function of the wavenumber k and round trip distance r, and is preferably the product kr.

There is also provided a radar system for measuring rotation of a target, comprising:

a) a linearly polarised transmit antenna configured to transmit a linearly polarized radar signal towards a target, wherein the target manipulates the phase of the radar signal depending on its orientation around an axis defined by the direction of propagation of the transmitted radar signal;

b) a linearly polarized receive antenna configured to receive a scattered signal from the target, wherein the scattered signal is circularly or elliptically polarised;

V_rx = +^me^jkre^j2cl) [Eq. 3] where V_rx is the voltage received by the receive antenna; m is a normalisation factor; j is the imaginary unit; k is the wavenumber of the radar signal; r is the round trip distance from the transmit antenna to the target and back to the receive antenna; and φ is the phase change in the received signal.

Again the system may advantageously also include said target, wherein said target has a scattering matrix defined by:

S_hlx = me^,a j [Eq. ⁴1 wherein a is a function of the wavenumber k, round trip distance r, and phase φ.

Preferably, said target has a scattering matrix defined by:

^{1 ±j}] [+j -iJ [Eq. 5]

A preferred embodiment of either system, according to the aspects defined above, further includes:

the transmit antenna, or a second transmit antenna, being configured to transmit a second signal, having the same polarization state (elliptical or linear) as the previously defined transmit antenna of the respective system, but of a different frequency;

a second receive antenna configured to receive a second scattered signal from the target at that different frequency;

signal processing means for measuring a second phase change for the second received signal over time; and wherein said processor is processor programmed to calculate from the first and second phase changes a frequency independent phase change component attributable to the change in φ, and a frequency dependent phase change component attributable to the change in kr, and thereby determining both the change in distance and the change in orientation.

Brief Description of the Drawings

The invention will now be further illustrated by the following description of embodiments thereof, given by way of example only, with reference to the accompanying drawings, in which:

Fig

1A is a schematic view of a first radar system and target, in isometric view;

IB is a schematic view of the radar system and target of Fig. 1A, in side view;

Fig is a schematic view of a second radar system and target of the invention;

Fig. 3 is a block diagram of the components of the radar system of Fig. 2;

Fig

Fig is a graph of measured voltages at the receive antenna when the target of Fig. 2 is positioned horizontally and vertically;

is a block diagram of a dual frequency radar system;

is a schematic view of a third radar system and target, in isometric view;

is a perspective view of a target;

is a front elevation of the target of Fig. 7; and is a graph of the received signal phase against orientation angle, for a linearly polarized incident radar wave scattered by the target of Figs. 7 and 8 and as measured by a linear polarizing receiving antenna.

Detailed Description of Preferred Embodiments

In Fig. 2 there is illustrated, generally at 30, a system according to the invention comprising a continuous wave, circularly polarised Tx/Rx radar 32, having circularly polarizing transmit antenna 34 and receive antenna 36. A transmitted circularly polarized signal (incident signal) 38 with electric field Ei is transmitted and a linearly polarized signal (scatter signal) 40 with electric field Es is received by the radar 32.

The incident field is described by:

[Eq. 6] where h_tx is the electrical length of the transmit antenna. The vector in Eq. 6 corresponds to vertical and horizontal polarization and describes a left-handed circularly polarized wave

The target is a dipole target 42, which rotates about an axis e_z which coincides with the line from the radar to the target (it is assumed that the distance r from radar to target is many times greater than the separation between antennae). As shown in Fig. 2, the dipole target is lying along a horizontal axis e_h, parallel to the wavefront of the incident signal. This is referred to as the horizontal position. The angular arrow with indication φ shows the target rotating through degrees about the axis e_z until it lies along the orthogonal axis e_y, i.e. to the vertical position.

The dipole target has a scattering matrix S_dip described by:

’dip = me jkr

COS²0 cos φ sin φ cos φ sin φ sin²0 [Eq. 7] where m, j, k and r are as previously defined and where φ is the angle between the reference position and orientation of the target, with a horizontally oriented dipole represented by φ=0.

When in the horizontal position, the target will scatter the incident wave most strongly when the electric field Ei at the target position is horizontal, and most weakly when it is vertical.

Because of the shape of the target the electric field Es of the scattered signal 40 is horizontally polarized as long as the target is horizontal.

When in the vertical position, the target will scatter the incident wave most strongly when the electric field Ei at the target position is vertical, and most weakly when it is horizontal. Because of the shape of the target the electric field Es of the scattered signal 40 is vertically polarized when the target is vertical.

The scattered electric field Es is described by:

Es = SdipE; = -^ru/eM

COS Φ sin0 [Eq. 8]

This field is detected at the circularly polarized receive antenna as a voltage V_rx:

V_rx = h/_xE_s = e^72<^ [Eq. 9]

Accordingly, for a stationary target, the voltage signal can be processed in known manner to derive the phase angle φ. In general, the absolute phase will not be known and thus the absolute angular position of the dipole target is unknown without additional information.

However, changes in phase can be readily detected and thereby equated to angular changes of the target, which in turn can give a rotational velocity.

In Fig. 3 the radar system is shown in more detail as a block diagram. An RF generator generates a radar signal which is sent via a power divider 52 and amplifier 54 to a circularly polarized transmit antenna 56. Scattered or reflected return signals are received at a receive antenna 58, from which they are divided 60 and fed to a pair of mixers 62, 64. The mixers 62, 64, in combination with a phase shifter 66 operating on the output signal from the power divider 52, generate an in-phase received signal I and quadrature signal Q. in known manner. These signals I and Q. are filtered through low-pass filters 68, 70, and then digitized with analog-digital converters 72, 74 from which they are provided as digitized inputs 76, 78 to a processor 80. The processor determines the phase angle φ.

In Fig. 4 the voltage on the receive antenna is seen plotted against time for the target when it is horizontal (solid line), and overlaid on this is the voltage plotted for the target when it is vertical (broken line). Both plots are zeroed to the same point in the cycle of the transmit waveform.

Thus it can be seen that by measuring the phase shift the orientation of the target can be calculated.

The above derivations assume that the phase angle change is attributable to the rotation of a stationary target. If the target is moving then Eq. 1 shows that the rotation angle can be calculated using a dual frequency system, which can distinguish between the frequency-related phase change due to Doppler shift and the frequency-independent phase change due to rotation angle.

Fig. 5 shows a dual-frequency system, having a first radar circuit 82, operating at a first frequency fl, and a second circuit 84 operating at a frequency f2. Both circuits are identical to the circuit described in Fig. 3. Each circuit provides a respective digitized signal pair I, Qto a processor 86, which calculates from the signals the target distance r and the phase φ as shown, in accordance with a modified version of Eq. 1:

V_rx = -me^72kre^72<^ [Eq. 10]

In Eq. 10, the distance term r is the distance from transmit antenna to target and not round trip distance, hence the additional factor 2 in j2kr. This alternative expression can be used when the transmit and receive antennae are co-located, i.e. monostatic radars.

Fig. 6 shows an alternative system, in which linearly polarized radar waves are scattered by a circularly polarizing target. A CW radar 100 has a linearly polarizing transmit antenna 102 and a linearly polarizing receive antenna 104. Incident radar waves E, are directed to a target 106 and reflected back as scattered waves E_s to the receive antenna 104.

The target 106 is a planar helical conductor which is centred on an axis e_z which is normal to the incident wavefront. Also shown are two orthogonal axes namely a horizontal axis e_H and a vertical axis e_v. Rotation of the target about the axis e_z can be measured as an angle φ. The scattered radiation E_s is circularly polarized due to the scattering matrix of the target.

The incident electric field is described by:

[Eq. 11] where h_tx is the electrical length of the transmit antenna. The vector in Eq. 2 corresponds to vertical and horizontal polarization and describes a left-handed circularly polarized wave

The helical target has a scattering matrix S_h|_X described by:

+71

h.lx = me^jkre^j2^ +j [Eq. 12] where m, j, k and r are as previously defined and where φ is the angle between a reference position and the current orientation of the target.

The target will scatter the incident wave as a circularly polarized reflection with a phase that depends on the orientation of the target. The electrical length of the receive antenna is given by:

h

[Eq. 13]

The scattered electric field Es is described by:

E_s = S_ftixEi = +me^^re^

1+7 [Eq. 14]

This field is detected at the circularly polarized receive antenna as a voltage V_r,

V_rx = h£_xE_s = ±ime⁷'^kre⁷'^2<^ [Eq. 15]

Accordingly, for a stationary (albeit rotating) target, the voltage signal can be processed in known manner to derive the phase angle φ. In general the absolute phase will not be known and thus the absolute angular position of the helical target is unknown without additional information. However, changes in phase can be readily detected and thereby equated to angular changes of the target, which in turn can give a rotational velocity.

Figs. 7 and 8 show an alternative to a helical target, in perspective and face-on views, respectively. The target 110 consists of two identical double reflectors (dihedrals), i.e. two pairs of dihedral reflectors. In Fig. 8 the broken line box 112 outlines one pair of reflectors, comprising a first (lower) reflector with faces or planes 114,116, and a second (upper) reflector with faces 118, 120. A first seam 120 divides the faces 114, 116 of the first reflector, while a second seam 122 divides the faces 118, 120 of the second reflector.

Referring to Fig. 8, the other pair of reflectors is immediately alongside the pair already described, and can be seen to consist of a first (upper) reflector having two faces 126, 128, and a second (lower) reflector having two faces 130, 132. Again, for this pair, it can be seen that a first seam 134 is defined where the faces of the first reflector meet and a second seam 136 is defined where the faces of the second reflector meet.

The target is symmetrical about a central axis that intersects the target face at a centre point. If one defines a co-ordinate system of x, y and z axes, the central axis lies along the x-axis, the seams 122 and 134 are parallel to the z axis, and the seams 124, 136 lie in the y-z plane at an angle of 45 degrees to both the y and z axes.

The scattering matrix of the first reflector 114,116 of the first pair can be described with

Σι = ^me'^a [J

[Eq. 16]

Whereas the scattering matrix of the second reflector can be described with

[Eq. 17]

As shown with the broken lines in Fig. 7, indicating the positions of the respective seams 122 and 124 along the x-axis direction, there is an offset between these seams along the x-axis.

Specifically, the position of the seams along the x-axis differs by Λ/8, where λ is the wavelength of the radar signal employed with the target, leading to a phase shift between both scattering matrices of β — a = 90 ° . Therefore the scattering matrix of the pair becomes

Σί/ιίχ = ηΤ^α j

[Eq. 18]

This agrees with the scattering matrix of a left helix target. The right helix target can be constructed by a shift of —Λ/8 and exhibits the following scattering matrix:

Trhix = ^me'^a . [Eq. 19]

An arbitrary number of these double reflector pairs can be combined as long as all pairs are oriented in the same way and are located at the same position along the x-axis. As shown the embodiment of Figs. 7 and 8 has two pairs.

The factor a is a function of wavenumber k, round trip distance to target r, and phase φ.

If the target of Figs. 7 and 8 is illuminated by a linearly polarized wave along the negative direction of the x-axis and the scattered wave is received by a linearly polarized antenna with a polarization orthogonal to the incident wave, a rotation of the target around the x-axis changes the phase ofthe received signal linearly, as is demonstrated by a graphing of received signal phase versus target rotation angle in Fig. 9.

A target such as that illustrated in Figs. 7 & 8 can also be used with a dual-frequency radar system to determine both position/motion and orientation/rotation. The requirement that the seams be offset by one-eighth of a wavelength can, as indicated earlier, be replaced by an offset of (Μ ± 1/8)λ where M is an integer. Therefore with appropriate frequencies being chosen, to give two wavelengths Al and A2, a single offset distance D can satisfy the twin requirements of

D = (M ± 1/8) Al and D = (N ± 1/8) A2, with M and N both being integer values. Such an offset distance will cause the necessary phase shift at both wavelengths.

Claims

1. A method of measuring rotation of a target, comprising the steps of:

b) receiving a scattered signal from the target using an elliptically polarized receive antenna, wherein the scattered signal is linearly or elliptical ly polarised;

c) measuring a phase change of the received signal over time;

Vrx = ^mejkr β]2Φ [Eq. 1] where Vrx is the voltage received by the receive antenna; m is a normalisation

15 factor; j is the imaginary unit; k is the wavenumber of the radar signal; r is the round trip distance from the transmit antenna to the target and back to the receive antenna; and φ is the phase change in the received signal.

2. The method of claim 1, wherein the transmitted, el liptically polarised, radar signal is circularly polarised.

20

3. The method of any claim 1 or 2, wherein said target has a scattering matrix defined by:

’dip

COS20 cos φ sin φ cos<fi sin φ sin20 [Eq. 2] wherein a is a function of the wavenumber k and round trip distance r, and is preferably the product kr.

4. A method of measuring rotation of a target, comprising the steps of:

c) measuring a phase change of the received signal over time;

Vrx =+^mejkrej21) [Eq. 3]

Where Vrx is the voltage received by the receive antenna; m is a normalisation

5. The method of claim 4, wherein the received radar signal is circularly polarised.

6. The method of claim 4 or 5, wherein said target has a scattering matrix defined by:

'hlx j

[Eq. 4] wherein a is a function of the wavenumber k, round trip distance r, and phase φ.

7. The method of claim 6, wherein said target has a scattering matrix defined by:

Shix = me]kre]2<l} + . [Eq. 5]

8. The method of any preceding claim, wherein the transmitted signal is generated by a transmit antenna that is co-located with the receive antenna.

9. The method of any preceding claim, further comprising the step of providing said target

5 on a body such that the rotation of the body is measurable by the rotation of the target.

10. The method of any of claims 1-3 or claims 4-9, further comprising the steps of:

transmitting a second signal, having the same polarization state (elliptical or linear) as in step (a) of claim 1 or claim 4, respectively, but of a different frequency to the signal in step (a);

receiving a second scattered signal from the target at that different frequency, as in

10 step (b), measuring a second phase change for the second received signal over time; and determining from the first and second phase changes a frequency independent phase change component attributable to the change in φ, and a frequency dependent phase change component attributable to the change in kr, and thereby determining both the change in

15 distance and the change in orientation.

11. A radar system for measuring rotation of a target, comprising:

a) an elliptically polarised transmit antenna configured to transmit an elliptically polarized radar signal towards a target, wherein the target manipulates the phase of the radar signal depending on its orientation around an axis defined by the direction of

20 propagation of the transmitted radar signal;

d) a processor programmed to calculate a change in orientation of said target relative to said axis, said change in orientation being determined as an angle φ which is proportional to the phase change of the signal, the phase change being calculated

5 according to the formula:

Vrx = /nejkr[Eq. 1] where is the voltage received by the receive antenna; m is a normalisation factor; j is the imaginary unit; k is the wavenumber of the radar signal; r is the round trip distance from the transmit antenna to the target and back to the receive antenna; and

10 φ is the phase change in the received signal.

12. The system of claim 11, further comprising said target, wherein said target has a scattering matrix defined by:

’dip = me'a

COS20 cos φ sin φ cos<fi sin φ sin20 [Eq. 2] wherein a is a function of the wavenumber k and round trip distance r, and is preferably

15 the product kr.

13. A radar system for measuring rotation of a target, comprising:

a) a linearly polarised transmit antenna configured to transmit a linearly polarized radar signal towards a target, wherein the target manipulates the phase of the radar signal depending on its orientation around an axis defined by the direction of propagation of

20 the transmitted radar signal;

5 according to the formula:

Vrx =+^mejkrej2<f) [Eq. 3] where Vrx is the voltage received by the receive antenna; m is a normalisation factor; j is the imaginary unit; k is the wavenumber of the radar signal; r is the round trip distance from the transmit antenna to the target and back to the receive antenna; and

10 φ is the phase change in the received signal.

14. The system of claim 13, further comprising said target, wherein said target has a scattering matrix defined by:

SMx = me]a j tEcl· 41 wherein a is a function of the wavenumber k, round trip distance r, and phase φ.

15 15. The system of claim 14, wherein said target has a scattering matrix defined by:

Shix = meIkrel2<l> + . [Eq. 5]

16. The radar system of any of claims 11-12 or claims 13-15, further comprising:

the transmit antenna, or a second transmit antenna, being configured to transmit a second signal, having the same polarization state (elliptical or linear) as the transmit antenna of

20 claim 11 or claim 13, respectively but of a different frequency;

signal processing means for measuring a second phase change for the second received signal over time; and

5 wherein said processor is processor programmed to calculate from the first and second phase changes a frequency independent phase change component attributable to the change in φ, and a frequency dependent phase change component attributable to the change in kr, and thereby determining both the change in distance and the change in orientation.

17. A radar scattering target comprising one or more pairs of dihedral reflectors, wherein in

10 each pair a first dihedral reflector comprises first and second reflective planes meeting at a first seam, the first seam defining a first seam axis, and the second dihedral reflector comprises third and fourth reflective planes meeting at a second seam, the second seam defining a second seam axis which is rotated relative to the first seam axis, about a rotation axis orthogonal to the first and second seam axes, by an angle Θ. wherein the first and second seams are offset from each

15 other along the direction of the rotation axis, by an amount equal to λ(Μ ± 1/8) where λ is the wavelength of the radar signal with which the target is to be used and M is an integer.

18. A radar scattering target according to claim 17, wherein the target comprises more than one pair of dihedral reflectors, and wherein the first seam axis of each pair is parallel to the first seam axis of each other pair.

20

19. A radar scattering target according to claim 18, wherein the second seam axis of each pair is rotated relative to the first seam axis by the same angle Θ.

20. A radar scattering target according to any of claims 17-19, wherein the angle Θ is between 40 and 50 degrees, most preferably 45 degrees.

21. A radar scattering target according to any of claims 17-20, wherein the target comprises two pairs of reflectors disposed alongside one another, and the target is rotationally symmetrical about a central axis, such that the first reflectors are diagonally opposite one another across the central axis and the second reflectors are diagonally opposite one another

5 across the central axis.

22. A radar scattering target according to claim 21, wherein when the target is viewed from the direction of the central axis, each of the four reflectors presents a square shape, and the target is of the form of a 2x2 square centred on the central axis.

23. A radar scattering target according to claim 21 or 22, wherein the second seam axis of

10 each pair is co-linear and meets at the central axis.

23. A radar scattering target having a scattering matrix defined by:

f1 j [j -iJ [Eq. 4] wherein a is a function of the wavenumber k, round trip distance r, and phase φ.

24. A radar scattering target according to claim 23, wherein said target has a scattering

15 matrix defined by:

1 ±j] [+j -iJ' [Eq. 5]

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Application No: GB 1622442.0