Detection device

Abstract

The present invention discloses a detection device for discriminating between different materials, and a method for doing so. The device comprises an optical system having at least one optical focussing element and a receiving element. The receiving element is sensitive to electromagnetic radiation, typically in the millimeter wave band, and the optical system being arranged to focus incident energy from a scene onto the receiving element. The optical system comprises a prism element having a first surface and a second surface, the first surface being opposite the second surface. At least a portion of the first surface is positioned at an angle to the second surface. The angle varies between a minimum at a first position on the first surface and a maximum at a second position on the first surface.

Claims

1. A detection device for discriminating between different materials, comprising an optical system having at least one optical focussing element, an optical scanning element and a receiving element, wherein the receiving element is sensitive to millimeter-wave electromagnetic radiation, the optical system being arranged to focus incident energy from a scene onto the receiving element via the optical scanning element, wherein the optical scanning element is a transmissive prism, and has a first surface having a region with a continuously variable angle with respect to a second surface of the optical scanning element, wherein the continuously variable angle acts to provide a continuously variable scan of the scene, and wherein the prism is arranged to rotate around a central axis to provide a linear scan of the beam direction.

2. Detection device of claim 1 wherein the optical scanning element comprises a prism element having a first surface and a second surface, the first surface being opposite the second surface and at least a portion of the first surface being positioned at an angle to the second surface, and wherein the angle varies between a minimum at a first position on the first surface and a maximum at a second position on the first surface.

3. Detection device of claim 2, wherein the angle varies continuously across the first surface between the first position and the second position on the first surface.

4. Detection device of claim 2, wherein the first surface comprises an interface between the first position on the first surface and the second position on the first surface where the angle changes sharply.

5. Detection device of claim 2, wherein the prism is cylindrical in outline, such that the first surface and the second surface are planform circular and form the circular ends of the cylinder.

6. Detection device of claim 5, wherein the first surface is described using a Cartesian co-ordinate system with z parallel to the prism rotation axis and where the angle is described by: $\tan =\frac{\mathrm{dz}}{\mathrm{dr}},\mathrm{where}{r}^2=x^2+y^2$

7. Detection device of claim 5, wherein the prism has a central axis perpendicular to the first surface and the second surface, and wherein the prism is mounted so as to rotate around the central axis.

8. Detection device of claim 2, wherein the rotation of the prism generates a beam of electromagnetic radiation in a continuous linear scan.

9. Detection device of claim 2 wherein the prism is arranged in use to reflect energy emanating from the receive element from at least one of the first and second surface away from the receive element at all angular positions of the prism.

10. Detection device of claim 9 wherein the prism has a localised region thereon, a deviation in both the first and second surfaces from their curvature at other regions, whilst maintaining a continuously variable angle between the two.

11. A detection device as claimed in claim 1 wherein the device is arranged to detect radiation produced by the target, or radiation reflected from the target emanating from the surrounding environment.

12. A detection device as claimed in claim 11 wherein the amount of radiation within a detection bandwidth of the device in the environment is augmented using a noise source.

13. Method of detecting objects present in a scene by means of receiving millimeter-wave electromagnetic radiation from the scene, comprising: receiving a beam of electromagnetic radiation from the scene using an optical system; forming, from the received radiation, a beam of electromagnetic radiation internal to the sensor system; scanning the internal beam, and hence also the external beam, using a moving, rotating element comprising a transmissive prism having a surface wherein at least a portion of the surface is positioned at an angle to a notional plane running through the element, wherein the angle varies between a minimum at a first position on the surface and a maximum at a second position on the surface, and wherein the scanned internal beam produces, for at least a portion of the element's movement, a continuous scan of the external beam, and wherein the prism is arranged to rotate around a central axis to provide a linear scan of the beam direction.

14. A method as claimed in claim 13 wherein the moving element is a transmissive prism, and the surface constitutes a first surface, the prism also having a second surface, the first surface being opposite the second surface and at least a portion of the first surface being positioned at an angle to the second surface, wherein the angle varies between a minimum at a first position on the first surface and a maximum at a second position on the first surface.

15. Method of claim 14, wherein the scan produced by the prism occurs substantially in a first dimension, and further wherein a second dimension is scanned by effecting movement of the whole optical system.

16. Method of claim 13 wherein the beam formed from the received radiation is a collimated beam.

17. Method of claim 13 wherein the method is implemented on a device comprising an optical system having at least one optical focussing element, an optical scanning element and a receiving element, wherein the receiving element is sensitive to millimeter-wave electromagnetic radiation, the optical system being arranged to focus incident energy from a scene onto the receiving element via the optical scanning element, wherein the optical scanning element is a transmissive prism, and has a first surface having a region with a continuously variable angle with respect to a second surface of the optical scanning element, wherein the continuously variable angle acts to provide a continuously variable scan of the scene, and wherein the prism is arranged to rotate around a central axis to provide a linear scan of the beam direction.

Description

DESCRIPTION OF THE DRAWINGS

(1) The present invention will now be described in detail, by way of example only, and with reference to the accompanying drawings, in which:

(2) FIG. 1 is a schematic cross-sectional view of an optical system for use in a detection device in accordance with an embodiment of the present invention;

(3) FIG. 2 is a schematic side view of the surface of a prism for use in an optical system employed in embodiments of the present invention;

(4) FIG. 3 is a schematic representation of the surface of a prism shown in FIG. 2;

(5) FIG. 4 is a schematic perspective view of the prism shown in FIGS. 2 and 3; and

(6) FIG. 5 shows schematic representations of three alternative prism arrangements.

DESCRIPTION OF THE INVENTION

(7) In order to overcome the issues associated with increased sampling, signal to noise ratio, integration time and algorithm efficiency, the present invention proposes the use of a continuous scan created using a novel prism arrangement, as described in more detail below. A detection device for discriminating between different materials comprises an optical system having at least one optical focussing element and a receiving element. The receiving element is sensitive to millimeter-wave radiation, making it suitable for use in various applications where it is necessary to determine the presence of materials or to distinguish between materials. The optical system is arranged to focus incident energy from a scene onto the receiving element, and comprises a prism element in addition to a focussing element. The prism element has a first surface and a second surface, the first surface being opposite the second surface and positioned at an angle to the second surface. The angle varies between a minimum at a first position on the first surface and a maximum at a second position on the first surface. When the prism revolves the continuous change in the surface of the prism creates a beam of radiation that continuously varies its scan direction, as opposed to a number of discrete beams formed in an aligned manner.

(8) FIG. 1 is a schematic cross-sectional view of an optical system for use in a detection device in accordance with an embodiment of the present invention. The optical system 1 comprises a receiving element 2, in optical alignment with an afocal telescope arrangement 3, plus a scanning prism 10, and a quarter wave plate 5 to act as an isolator for reflections from the prism and a small convex lens 4 to focus radiation onto the receiving element. Other embodiments may forego the quarter wave plate if such reflections are not a problem. The afocal telescope arrangement 3 comprises a first convex lens element 7, and a concave lens 6. Each lens element is formed from a high density polythene material having a refractive index of approximately 1.5 in the millimeter wave band 30 GHz to 300 GHz. Radiation from the scene, that is the object or subject requiring analysis to discriminate between materials, is collected as a large diameter collimated beam by the afocal telescope 3, passing first through the large convex lens 7 and then the small concave lens 6, thus forming a smaller diameter collimated beam 8 upon exiting lens 6. The collimated beam passes through the prism 10, and then through the quarter-wave plate 5, converting from circular to linear polarisation. This collimated beam is then focussed onto the receive element 2 by the small convex lens 4. The preferred receive element is a millimeter-wave horn with a radiation pattern matched to the diameter of the small convex lens 4.

(9) The quarter wave plate 5 reduces the magnitude of any spurious emitted radiation due to the receive element/antenna 2, such as its own noise temperature or local oscillator leakage, that reflects from the prism 10 and is received back at the receive element 2 as a time varying signal. For example, if vertical polarisation is emitted by the receive element 2, it will be converted to for example right hand circular polarisation by the quarter wave plate 5 before reflecting off the prism 10 as left-hand circular polarisation. The quarter-wave plate 5 will then convert this left-hand circular polarisation to horizontal polarisation which will be rejected by the vertically polarised receive element 2. If the quarter wave plate is omitted, the system will receive linear polarisation rather than circular polarisation, but that makes no significant difference to the signature received in the typical wavebands of interest, however the system will be more prone to error due to receiving its own emission reflected off the prism. However, some embodiments may do without the quarter-wave plate 5. Other embodiments may seek to provide further reduction of the effects of spurious emitted radiation, by using the technique discussed in relation to FIG. 5, which may be used instead of, or as well as, the quarter wave plate 5.

(10) The prism element 10 is positioned between the concave lens element 6 and the quarter-wave plate 5 such that radiation exiting the concave lens element 6 is incident on the prism 10 before reaching the quarter-wave plate 5. The prism 10 has a first surface 11 and a second surface 12, the first surface 11 being opposite the second surface 12. The prism 10 is cylindrical in outline, such that the first surface 11 and the second surface 12 are planform circular and form the ends of the cylinder. The second surface 12 is plane. The prism 10 is provided with a central axis 13 that defines a z axis and perpendicular to the second surface 12, and is mounted so as to rotate around the central axis 13. The prism 10 is positioned with the central axis 13 laying below the collimated beam 8, such that only a portion of the prism 10 is positioned within the collimated beam 8 at any point during its rotation. Effectively only a portion laying between the central axis 13 and the circumference 14 of the circular prism 10 is within the collimated beam 8 at any one moment in time. Those portions of the prism involved in refracting desired radiation may be collectively termed the active part of the prism.

(11) As indicated above, the first surface 11 is positioned opposite the second surface 12. At least a portion of the first surface 11 is positioned at an angle to the second surface 12, and wherein the angle varies between a minimum at a first position 16 on the first surface 11 and a maximum at a second position 15 on the first surface 11. This is shown in more detail in FIGS. 2 and 3.

(12) FIG. 2 is a schematic side view of the surface of a prism for use in an optical system employed in embodiments of the present invention. The first surface 11 of the prism 10 is provided with a central flat hub portion 17 having a radius c, where the first surface 11 and the second surface 12 are positioned a constant thickness t apart. Between the central portion 17 and the circumference 14 of the prism 10 the angle () the first surface 11 makes with the second surface 12 varies with rotation angle : =arctan(y/x). In the cross-section shown an upper portion of the first surface 11 is inclined at an angle () to the second surface 12, and a lower portion of the first surface 11 is inclined at an angle +() to the second surface 12. The distance parallel to the z axis between the point closest to the central portion 17 and the point closest to the circumference 14 in the upper portion at the first position 16 is d.sub.min, and the distance parallel to the z axis between the point closest to the central portion 17 and the circumference 14 in the lower portion at the second position 15 is +d.sub.max. The flat central portion 17 is positioned at d.sub.min/2 or +d.sub.max/2.

(13) FIG. 3 is a schematic representation of the surface of a prism shown in FIG. 2. The first surface 11 is described using a Cartesian co-ordinate system, where any point on the first surface 11 may be described as a position in terms of (x, y). It is not possible to have a continuously varying surface across the whole of the prism, unless increases smoothly both from an minimum value to a maximum value and then back again which is undesirable due to increased curvature, and hence increased aberrations, as described above, therefore an interface 18 where the angle changes sharply exists, between the first position 16 and the second position 15. It is also desirable to have regions at either end of the scan i.e. on either side of the interface 18 where the angle between the first surface 11 and the second surface 12 does not change, essentially forming two flat ends to the scan. This avoids the signal to noise ratio at the edges of the scan from being worse than in the rest of the scan. The flat ends occur where 0, and when 22. The radius of the entire prism 10 may be described by , and the equations defining the surface of the prism 10 in radians are:

(14) $r=\sqrt{x^2+y^2}$$=\mathrm{arc}\tan \left(\frac{d_{\min }}{-c}\right)$$=\mathrm{arc}\tan \left(\frac{d_{\max }}{-c}\right)$

(15) Solving these equations for gives:

(16) $=\text{:}$$=+\left(-\right)\left(\frac{-}{2--}\right)\text{:}<<2-$$=\text{:}2-$$=\mathrm{arc}\tan \left(y/x\right)$

(17) To ensure that all of the values of between 0 and 2 are obtained:
=arctan|y/x|:x>0,y>0
=arctan|y/x|:x<0,y>0
=+arctan|y/x|:x<0,y<0
=2arctan|y/x|:x>0,y<0

(18) The surface sag (z axis coordinate) is given by

(19) $\mathrm{sag}=t-\left[r-\left(\frac{c+}{2}\right)\right]\tan$

(20) OSLO (Optics Software for Layout and Optimisation, available from Lambda Research Corporation, 25 Porter Road, Littleton, Mass. 01460, USA, optimised for version 6.0.1) is a software tool used to design lenses, although it will be appreciated by those of ordinary skill in the art that other suitable software packages are available. Using such a program, user defined surface macros, which return a function Uds_f=0, can be set up to describe the surface:

(21) $\mathrm{Uds\_f}=z-\mathrm{sag}=z-t+\left[r-\left(\frac{c+}{2}\right)\right]\tan \text{:}r>c$$\mathrm{Uds\_f}=z-t\text{:}rc$

(22) OSLO also requires the partial derivatives with respect to x, y and z of Uds_f as follows, providing r>c:

(23) $\mathrm{Uds\_f}=z-t+\left[r-\left(\frac{c+}{2}\right)\right]\tan$$\begin{array}{c}\frac{d}{\mathrm{dx}}\mathrm{Uds\_f}=\left[r-\left(\frac{c+}{2}\right)\right]\frac{d}{\mathrm{dx}}\tan +\tan \frac{\mathrm{dr}}{\mathrm{dx}}\\ =\left[r-\left(\frac{c+}{2}\right)\right]{\sec }^2\frac{d}{\mathrm{dx}}+\tan \frac{d}{\mathrm{dx}}\sqrt{x^2+y^2}\end{array}$$\mathrm{Now}$$\frac{d}{\mathrm{dx}}=0\text{:}$$\frac{d}{\mathrm{dx}}=\left(\frac{-}{2--}\right)\frac{d}{\mathrm{dx}}\text{:}<<2-$$\frac{d}{\mathrm{dx}}=0\text{:}2-$$\mathrm{So}$$\frac{d}{\mathrm{dx}}\mathrm{Uds\_f}=\frac{x}{r}\tan \text{:}$$\frac{d}{\mathrm{dx}}\mathrm{Uds\_f}=\left[r-\left(\frac{c+}{2}\right)\right]\left(\frac{-}{2--}\right)\left(1+{\tan }^2\right)\frac{d}{\mathrm{dx}}+\frac{x}{r}\tan \text{:}<<2-$$\frac{d}{\mathrm{dx}}\mathrm{Uds\_f}=\frac{x}{r}\tan \text{:}2-$$\mathrm{Also}$$x=r\cos y=r\sin$$1=\frac{\mathrm{dr}}{\mathrm{dx}}\cos -r\sin \frac{d}{\mathrm{dx}}$$y\frac{d}{\mathrm{dx}}=\frac{x^2}{r^2}-1$$\begin{array}{c}\frac{d}{\mathrm{dx}}=\frac{x^2-y^2}{{\mathrm{yr}}^2}\\ =\frac{-y}{r^2}\end{array}$

(24) Similarly:

(25) $\frac{d}{\mathrm{dy}}=\frac{x}{r^2}$$\mathrm{So}\mathrm{given}r>c,\frac{d}{\mathrm{dx}}\mathrm{Uds\_f}=\frac{x}{r}\tan \text{:}$$\frac{d}{\mathrm{dx}}\mathrm{Uds\_f}=\frac{x}{r}\tan -\left[r-\left(\frac{c+}{2}\right)\right]\left(\frac{-}{2--}\right)\frac{y}{r^2}\left(1+{\tan }^2\right)\text{:}<<2-$$\frac{d}{\mathrm{dx}}\mathrm{Uds\_f}=\frac{x}{r}\tan \text{:}2-$

(26) Similarly:

(27) $\frac{d}{\mathrm{dy}}\mathrm{Uds\_f}=\frac{y}{r}\tan \text{:}$$\frac{d}{\mathrm{dy}}\mathrm{Uds\_f}=\frac{y}{r}\tan +\left[r-\left(\frac{c+}{2}\right)\right]\left(\frac{-}{2--}\right)\frac{y}{r^2}\left(1+{\tan }^2\right):<<2-$$\frac{d}{\mathrm{dy}}\mathrm{Uds\_f}=\frac{y}{r}\tan \text{:}2-$$\mathrm{If}r<=c$$\frac{d}{\mathrm{dx}}\mathrm{Uds\_f}=\frac{d}{\mathrm{dy}}\mathrm{Uds\_f}=0$

(28) Also for all r and ,

(29) 0$\frac{d}{\mathrm{dz}}\mathrm{Uds\_f}=1$

(30) These equations can then be used to define the first surface 11 of the prism 10.

(31) FIG. 4 is a schematic perspective view of the prism shown in FIGS. 2 and 3. This illustrates that the angle between the first surface 11 and the second surface 12 varies continuously form a minimum to a maximum value during one revolution of the prism 10, apart from at each flat end. The interface 18 where the angle changes sharply only intersects the 32 mm diameter radiation beam transiting the 100 mm diameter prism for 16% of the rotation of the prism if the beam is offset by 33 mm from the prism axis, thus the prism is relatively efficient with only 16% dead time.

(32) In this embodiment the maximum thickness of the prism 10 is 12.044 and the minimum thickness 2 mm when formed from a polythene material having a refractive index of approximately 1.5 in the millimeter-wave band to enable it to be used with existing optical systems. The diameter of the prism is 100 mm, d.sub.max=d.sub.min=10.044 mm, c=15 mm, t=7.022 mm and ==54.17 degrees. The prism is used with an afocal telescope of aperture 150 mm forming a collimated beam through the prism of diameter 32 mm, and the effect of the prism is to scan the instantaneous vertical field of view of the afocal telescope through approximately 1.9 degrees. This is equivalent to collecting data over 6 beamwidths of the afocal telescope when operating at the preferred frequency of 183 GHz.

(33) In order to integrate the data obtained to reduce noise and therefore increase the signal to noise ratio a rolling average of the data obtained is taken over a single rotation of the prism 10, although a matched filter may be used as an alternative. This results in a reduction in signal to noise ratio of a factor of approximately 1.51, compared with that of the standard two-spot system described in U.S. Pat. No. 7,271,899. However this compares very favourably with the signal-to-noise reduction by a factor of 1.95 for a prism made of 4 discrete zones scanning the afocal telescope over only 4 beamwidths rather than 6 beamwidths. The optical performance of the prism 10 in the preferred embodiment is diffraction limited throughout the field of view, with Strehl intensity of at least 85% predicted by OSLO throughout the field of view. A small sideways deflection of the collimated beam 9 is generated, but is equivalent to 0.1 in object space and varies little with scan position, so has little overall effect on the data obtained.

(34) In use, the prism is employed in a method of detecting objects present in a scene by means of receiving millimeter wave radiation from the scene. Levels of threat (the presence of various materials) are determined from the radiometric temperature of the scan, with variations in temperature within the continuous linear scan being compared with each other to determine the threat level. The processing of data received from the scene is discussed in more detail below. A collimated beam 9 of millimeter wave radiation from the target is collected by the afocal telescope. The scene is then scanned in a first direction by moving the whole optical system. The internal collimated beam 8 is scanned using the prism element 10 described above, and this in turn causes the collimated beam 9 to form a continuous linear scan in a second direction, the second direction being perpendicular to the first direction. So, if the first direction of the collimated beam 9 is horizontal, scanning across the scene, the second direction in which the beam is spread is vertical. As an alternative, if appropriate and desired, the first direction may be vertical and the second direction may be horizontal. Only a single scan movement of the whole optical system is therefore required.

(35) Note that if the prism angle cannot be considered to be small, and a scan linear with time is required, then if is the angular deviation of mm-wave radiation caused by the prism, strictly the requirement is

(36) $={}_{\min }+\left(\frac{{}_{\max }-{}_{\min }}{2}\right)$

(37) Where .sub.min and .sub.max are the end of scan angular radiation deviations towards the axis and away from the axis respectively.

(38) Given that the front face 12 of the prism is flat (as per the typical implementation), then the prism angle may be found using:
=arcsin(n sin )
where n is the refractive index of the material the prism is made from. and may be found similarly from .sub.min and .sub.max.

(39) Various algorithms may be used to process the data obtained using the optical system 1 described above. Data is output in a continuous stream from the receiving element at time intervals T from the commencement of the prism scan until its termination. The scan is used to determine threat points in relation to the radiometric temperature of the scan, that is, a low temperature point represents a high threat, in other words, a material requiring investigation is present, and a high temperature point represents a low threat. This may be used, for example, when scanning a subject for a weapon or explosive material at an airport or other secure location.

(40) The simplest way to process the data is to average the input data stream y.sub.i into overlapping segments w units wide spaced w/2 apart, where w is the collimated beam 9 width (full-width half maximum FWHM).

(41) Each point at which a difference in materials resulting in a threat level will be calculated has a signal given by:

(42) $V_j=\frac{\underset{i=i{\min }_j}{\overset{i{\max }_j}{.Math.}}{y}_i}{i{\max }_j-i{\min }_j+1}$

(43) Where V.sub.j is a signal at a threat point j,

(44) $c\left(j\right)=\frac{j\left(q+1\right)}{n+1}$
is the index of the centre time point at the centre of threat point j, q is the number of time steps per scan, and

(45) $r=\frac{w-1}{2},$
i min.sub.j=int(c(j)r+0.5),i max.sub.j=int(c(j)+r+0.5).

(46) Rounding causes the threat points to be spaced in a non-uniform manner, but the worst case error should correspond to <T/2. For a six-spot scan with eleven points, and T=1.56 ms, a beam width corresponds to 9 points, therefore the centre of the average will only be in error by 1/18 of a beam width. A Gaussian filter of the form

(47) $g\left(x,w\right)=\frac{\sqrt{\ln \left(16\right)}}{w\sqrt{}}{e}^{\frac{-4\ln \left(2\right)x^2}{w^2}}$
may be used, where w is the full width at half maximum of the Gaussian. It is sufficient to use points with x ranging from w to w, where the units used are time, time step number, or number of beam widths, as desired. Other algorithms, such as those based upon averaging between temperature points in a scan, determining a mean temperature or deviation from a mean temperature may be used as alternatives for determining a threat level from the data received from the receiving element.

(48) In the above embodiment a single variation of angle between a minimum and a maximum is used. However, it may be desirable to vary the angle between more than one minimum and maximum point, for example, where two such variations are included in a single rotation of the prism 10, however this tends to increase optical aberration. It may also be desirable that rather than only a portion of the first surface 11 being positioned at an angle to the second surface 12 that the flat central portion 17 is removed, and the whole of the first surface 11 is positioned at an angle with respect to the second surface 12 where the angle varies continuously between a minimum at a first position on the first surface 11 and a maximum at a second position on the first surface.

(49) FIG. 5 shows three examples of prisms that are designed to prevent retro-reflections of energy emanating from the receive element, and which may be used in embodiments of the present invention. The prisms have an active portion in a radial band around their centre, not including the centre itself, which is used to scan energy from a scene onto the receive element as shown in FIG. 1, in broadly similar fashion to the prism of FIG. 2. All these prisms of FIG. 5 however are arranged to prevent retro-reflection of energy back towards the receive element. In each case the radial gradient of the prism is constant, i.e. dz/dr is constant for any one value of rotation angle , where sag is in the axial z direction and r.sup.2=x.sup.2+y.sup.2 (where the co-ordinate system is shown in FIG. 5f).

(50) FIG. 5a shows a first prism 50 that has a first surface 51 and a second surface 52 that have (as with the other prisms shown herein) a continuously varying angular relationship to each other as the prism is rotated about its axis (the z axis). Thus, energy that passes through a part of the prism in the z direction is refracted according to known principles by an amount dependent upon the angular difference between the first and second surfaces. The angular relationship of the first and second surfaces is chosen so as to provide a linear scan of the energy emanating from a remote target onto the receive element. It will be seen that, in contrast to the previously shown embodiments, the prism has a generally conic form, having a slope in the z axis as it moves along a radius line, in both the first and second surfaces. The slope is chosen so that retro-reflection from the receiver element does not occur at any position during a full rotation of the prism.

(51) FIGS. 5b and 5c show two views of a prism 55 having first 56 and second 57 surfaces that again have a continuously varying angular relationship between each other, and so act to provide a linear scan of energy passing through an active portion the prism. The prism 55 has a linear deviation 58 in the z axis around the point in where the first and second surfaces are parallel to each other. It will be seen that energy impinging upon a surface 56 of the prism and arriving parallel to the axis thereof will be reflected back dependent upon the angle of the surface 56, and (via refraction through the material of the prism) of the angle of the surface 57. Where the deviation 58 (as compared to the prism of FIG. 2) occurs, the angular relationship between the two surfaces is the same as in the other parts of the prism, hence scanning of the beam occurs as before but the faces are no longer parallel to the axis of the prism, and so there will be no retro-reflection back to the receiver element.

(52) FIGS. 5d and 5e show a further embodiment of a prism designed to avoid retro-reflections. Again, the prism has two surfaces, that have a constantly varying angular relationship to each other, seen as the prism rotates as before. It is broadly similar to the embodiment of FIGS. 5b and 5c, but differs in that instead of having a linear deviation in the z axis at a region where the two surfaces become parallel to each other, it has a gradually changing deviation. This avoids the sharp transitions of the embodiment of FIG. 5b, which might reduce refracted image quality, A circumferential profile of the form (1+cos ) is used in the deviation region, although it will be appreciated that other curves could also be used, as would be understood by a normally skilled person.

(53) Describing this embodiment more precisely, then assuming the prism interface (as defined in relation to ref. 18 in FIG. 3) is at =0 and the deviation region starts and finishes at =180, then a suitable equation for change in sagi.e. the z coordinate of the surface (compared to the standard prism of FIG. 2, for both surfaces)is

(54) $z=G\left(r-c\right)\frac{{\left[1+\cos \left(\frac{180\left\{-180\right\}}{}\right)\right]}^n}{2^n}\text{:}r>c,.Math.-180.Math.<$$z=0\text{:}\mathrm{elsewhere}$
where an inner radius of the active region of the prism is c, G is the maximum desired radial gradient of the deformation (e.g. to keep the prism inside a desired size envelope) i.e. G=dz/dr at =180, and n>0.5 is chosen for optimum performance. The value of n and are advantageously chosen to minimise the peak retro-reflected energy over a complete revolution of the prism, and may be done by running simulations with suitable optical design software. Smaller values of p reduce the angular extent over of the deviation, and larger values of n increase the gradient of the deviation over near the centre of the deviation at the expense of the gradient near the edges of the deviation, i.e. sharpen the peak of the deviation. A value of n greater than 0.5 is beneficial in that it gives a smooth transition between the deviated and non-deviated parts of the surface.

(55) The materials from which the prism and lenses may be made will depend upon the exact optical qualities required, and may be selected according to their loss, and refractive index, to provide desired optical characteristics. Although polythene has been used in the embodiments described above, other materials, such as PTFE, Rexolite or other plastics, as would be understood by those of ordinary skill in the art.

(56) These and other embodiments of the present invention will be apparent from the appended claims.