Patent Application
20070269071
The invention relates to apparatus and methods for creating a sound field, preferably using arrays of sonic output transducers. The invention concerns the development of an array having a curved surface.
In several co-owned international published patent applications, e.g. WO01/23104, WO02/078388 acoustic digital delay array loudspeaker systems (hereinafter referred to as digital-delay array antennas (DDAA) or more simply as Arrays) are described, most of which are planar or substantially planar in their arrangement of the transducers comprising the Array. Some variants described have the Array supplemented with one or more additional (often “woofer” type) transducers which may or may not be substantially within the plane of the Array proper, but these generally provide auxiliary functions such as non-steered reproduction of low frequencies (“bass”). In another co-owned patent application (EP 0,818,122-A) a non-planar Array is described wherein multiple successive “layers” of transducers are placed one behind the other, each successive further-from-front layer emitting its sound via “gaps” in the layer or layers in front of that layer, thus building up a three-dimensional (3D) Array of transducers. However, the effective radiating surface in this case is just the outer layer of transducers plus its radiating gaps (emitting radiation from the transducers behind) which is therefore effectively planar. Essentially planar Arrays with some slight curvature in the 2D surface containing the radiating elements are also anticipated in these applications. However no development of these arrays has taken place. It was thought that it is best to minimise the curvature of the Array so as to avoid “shadowing” of certain transducers from certain beam angles (i.e. positions in the near or far field where certain transducers are no longer visible because of occlusion by the front surface of the curved Array), and also because real transducers have finite beam-width of their own at the higher frequencies due to their radiating diameters becoming comparable in size with the wavelength of radiated sound, and thus individual transducers begin to beam in their individual “straight-ahead” directions. In a planar Array such individual transducer beaming directions at least all point in substantially the same direction and cause more predictable effects on the beam shape and radiated power.
Also known for planar arrays is the technique of Apodization, or Windowing or element-weighting. Essentially, Apodization is a technique whereby quite separately from the differential timing of signals to each array element (determined by the required beam direction and shape requirements), the elements are also additionally each given a possibly unique “weight” or gain setting (nominally in the range 0 to 1, or more generally in the range −1 to +1), in order to further refine the beam shape. If all these weights w are unity, then the array is said to be unweighted, or non-apodized. Typically, a non-apodized array will produce a narrow beam but with significant side-lobes (unrelated to alias sidelobes which are due to too coarse a spacing of array elements). A useful apodization weights the array elements down more, the further they are from the centre of the array, and in some cases the array weights w taper towards zero at the edge of the array. When this is done, the array beam becomes somewhat broader, but the sidelobes can be very greatly reduced in amplitude, by many tens of dB. This works essentially because an unweighted array has an abrupt change in signal sensitivity (whether transmitting or receiving) at the edges of the array, where the change is from w Oust within the edge of the array) to zero Oust outside the array). Because the beam pattern is related to the Fourier transform of the aperture “illumination function” (essentially proportional to the aperture weighting or apodization function), any abrupt change in the one will lead to sinc function-like (sinc==sin(x)/x) or sinc2 function-like oscillations in the other, which manifest themselves as beam sidelobes. By tapering (i.e. applying weighting to) the edges of the aperture (with common functions such as raised cosines, or even linear tapers towards the aperture edge) the Fourier transform of the illumination function has reduced ripple, and thus the antenna has reduced sidelobes. Such a tapering function is shown in
Furthermore, if an antenna beamshape is required that is essentially flat over some angular distance, then again, noting the Fourier transform relation between the domains, it is clear that a sinc weighting of the aperture (where some weights w are negative) will have the desired effect, as the Fourier transform of a sinc function is a square pulse (i.e. flat topped).
However, all of the above described prior art applies only to planar, or flat, DDAAs. In this invention we consider non-planar DDAAs, where the array elements are no longer arranged on a plane, but more generally on a 3D surface of some kind, or more generally still, throughout a 3D volume. In what follows we describe an apodization technique that solves some hitherto unforeseen problems with 3D arrays, as exemplified by a cylindrical DDAA (where the transducer elements of the array are arranged in some pattern (not necessarily uniform) over the surface of a cylinder), but it should be noted that the techniques described are generalisable to all 3D DDAA structures, with uniform or nonuniform element distributions, whether for receiving or transmitting DDAAs, and whatever form of waves (e.g. acoustic, electromagnetic, other) are being transduced, and are to be included as part of the invention.
Arrays of the present invention are preferably deliberately highly curved in 2D and 3D and take advantage of the effects of individual transducer beaming directions where relevant. Such curved arrays can usefully be cylindrical, conical, spherical, ellipsoidal, or other 2D surface and 3D bulk/solid distributions of transducers, and sections of such closed surfaces—e.g. hemispheres, spherical caps, half, quarter, three-quarter etc cylinders and cones, and other segments of complete surface and volume distributions of transducers.
In a first aspect of the invention, there is provided an apparatus for creating a sound field, said apparatus comprising: an array of sonic output transducers, which array is capable of directing at least one sound beam in a selected direction; wherein said transducers lie on a curved surface subtending 90° or more. Preferably, the transducers have their primary radiating direction perpendicular to the tangent of the curved surface at the point where they lie. The “primary radiating direction” is the direction which emits the maximum sound pressure level for that transducer. For standard cone transducers, the primary radiating direction is a line parallel to the longitudinal axis of the transducer, which line forms the rotational axis of symmetry for the transducer.
The curved surface is preferably a physical surface, which is to say the transducers are embedded in the surface such that the gaps between the transducers are filled with material. Alternatively, gaps between the transducers may not necessarily be filled with material or any such material in the gaps need not follow the curvature of the surface.
The digital delay array loudspeaker preferably comprises 4 or more transducers arranged in space in a substantially non-planar fashion, preferably with all transducers positioned such that their 3D centres of gravity lie in some smooth 3D highly curved surface, the 3D surface being open or closed. The curvature of the surface preferably has a single sign over its whole extent, which is to say that the curvature of the surface preferably does not change. The curvature of the surface is preferably convex with the transducers emitting sound out of the convex face of the surface. Preferred examples of such surfaces are cylinders, spheres, cones and segments thereof. The transducers are preferably each driven by a discrete signal processing channel including a uniquely selected per-transducer signal delay as per conventional prior-art Arrays, this delay being a function of the three-dimensional (3D) spatial position of the effective centre of acoustic radiation of that transducer (the transducer Position) and also a function of the beam shape that is to be produced by the Array; the signal amplitude sent to each transducer by its signal-processing channel is a function of the beam shape to be produced and possibly also a function of the Position of the transducer.
Where it is desired for the Array to produce a beam focussed on a point in space (Focal Point) then the signal processing delay (Delay1) for each transducer of the Array used to form the beam, is chosen such that this delay plus the respective delay (Delay2) caused by time-of-travel of sound from the Position of said transducer to the Focal Point (which latter delay is in general a function of the Position of said transducer) is a constant value for all transducers in the Array. Where other beam shapes are required, more complex Delay1 selection rules are needed.
Which transducers of the Array are used for the generation of any particular beam is largely a matter of choice, with the proviso that the more transducers of the Array used for a beam, the greater energy possible in the beam, using only those transducers which have line of sight to a point on the line of beaming direction, such as the Focal Point is preferable (as the remainder will only contribute to the energy at the Focal Point via diffraction, refraction and/or reflection), and the greater the physical separation in a plane normal to the beam direction of the set of transducers used to form a beam, then the higher the spatial resolution achievable, and finally the more tightly packed (i.e. the smaller the inter-transducer separation of neighbouring transducers used for a beam) the set of transducers used to form a beam, then the higher the frequency of sound that may be beamed without grating sidelobes forming. The transducers used are preferably only those that have an unimpeded component of radiation in a direction which contributes to the desired beam. In other words, transducers which are “shadowed” are not used and are preferably de-energised.
Multiple independent beams may be supported by the non-planar Array simultaneously, each carrying independent audio programme material and each being independently steerable and focussable, as is known in the prior art for planar Arrays, with the unique advantage that with the non-planar Array, the possibility of pointing separate beams simultaneously in essentially opposite directions becomes possible (a planar Array with a closed back is incapable of producing a beam in the half space behind the Array, i.e. the half space opposite to the direction in which the principal transducer radiation axes point; a non-planar Array of the present invention removes this limitation, completely in the case that the Array is a closed surface rather than just a segment of such a surface). The detailed acoustic construction of such curved Arrays can vary greatly, but effectively the “rear” acoustic radiation of each transducer in such an array is most preferably “contained” (i.e. prevented from contributing significantly to the externally felt radiation), either by setting each transducer into the otherwise closed-surface of a shared volume of fluid, generally air, or alternatively, by separately enclosing the rear of each transducer in its own closed volume. In either case, there are generally radiation efficiency advantages in having the transducer frontal radiating areas protrude from a commonly shared otherwise closed-surface.
The curved surface of the array preferably subtends more that 90°, such as 180° or 360°, so as to form a cylindrical array.
Thus for example, a cylindrical Array with transducers uniformly distributed over the cylinder's curved surface and where the circumference of the cylinder is large enough to accommodate more than two transducer diameters around it, and where the length of the cylinder is great enough to accommodate at least one transducer diameter (but preferably more, such as three or more), may be mounted with its axis vertical, in which case approximately half of the transducers (i.e. those half closest to the Focal Point where the focal distance is positive, and those half furthest from the Focal Point where the focal distance is negative, i.e. a virtual focus) may usefully be driven to project a sound beam to a focus in any horizontal direction (including the case where the Focal Point is at ±infinity). Preferably, six transducers or more are spaced apart around the circumferential direction of the cylinder.
Unlike with a planar Array where it is generally useful to recruit all of the transducers in the Array for a beam produced in any (possible) direction, with the non-planar Arrays of this invention it is advantageous to perform an additional step in the beam forming process, which is to calculate which of the Array's transducers may usefully contribute to a beam pointing in any specific direction, and then to only drive power for that beam into that subset of the transducers of the Array. Thus when sweeping a beam across a range of angles, two simultaneous processes are preferably carried out: 1) recalculating which transducers of the Array should be used for the beam as the direction changes. 2) recalculating the delays for each transducer participating in the beam so that the beam is produced in the desired direction; this additional process (transducer selection) is a new feature of the present invention. As described above, the method of calculating for each transducer whether or not it should be recruited for a given beam direction is essentially to compute whether or not that transducer has a line of sight to a point in the sound field, e.g. to the Focal Point—if it has it should be recruited for that beam direction, if not, it should preferably not be used. Refinements of the method may also take account of the frequency range being transmitted in the beam and the directionality of any given transducer at the upper frequency end of that range. Where a transducer with a line of sight to the Focal Point has a diameter large enough that it becomes highly directional at the upper end of the frequency range and is pointing in a direction sufficiently away from the direction to the Focal Point that its radiation pattern is weak (e.g. more than 3 dB down, or more than 6dB down) in the direction of the Focal Point, it may be advantageous to exclude that transducer from that beam direction as little will be gained by including it and transmission power will be wasted.
The first aspect thus also provides a method for creating a sound field, said method comprising: providing an array of sonic output transducers which lie on a curved surface subtending 90° or more; and directing a beam of sound using said array.
Returning to the example cylindrical Array described above, where the length of the cylindrical Array parallel to its axis is several to many transducer-diameters long, then the Array so formed will have significant directivity in a plane running through (and parallel to) the cylinder axis at sufficiently high frequencies (where the cylinder length is ˜>=wavelength of sound). New possibilities are now opened up for Arrays of the present invention, not possible with prior art planar arrays. For example, if the beam forming delays applied to transducers are now a function only of their distance along the axis of the cylinder of the array (and not a function of their angular displacement around the cylinder), then the Array will transmit a beam simultaneously (i.e. a fan beam) in all directions perpendicular to the cylinder axis, while the beam shape at right angles to this plane (i.e. in planes passing through and parallel to the axis) may be tailored by choice of delay function. Specifically a pencil beam in this plane may be achieved at any angle (latitude) from −pi rads to +pi rads relative to a plane perpendicular to the cylinder axis) whereupon the Focal Point previously described will open out into a Focal Circle (symmetrically positioned about the cylinder axis). Where the cylindrical Array is vertically disposed some distance above a nominally planar floor or ground surface, variation of the latitude angle will vary the distance from the Array where the beam intersects the floor. Choice of different delay functions can vary the beam shape around the beam direction independently of varying this beam (axis) intersection distance. Thus very flexible flood-coverage of floor areas is possible with such an Array. Furthermore, by selectively excluding some transducers at certain angles around the cylinder (longitude angles) from the beam, and/or by suitably applying delays to each transducer which are also a function of longitude angle, the otherwise circularly symmetric fan beam can be converted into a sector-of-circle fan beam, or indeed into several multiple sector fan beams, and the latitude angle of each such sector fan beam may be independently chosen.. Thus great selectivity of which areas of the surrounding ground/floor are covered by the beam or beams is possible. Furthermore, separate adjacent or non-adjacent regions of the surroundings may be flooded with different audio programmes simultaneously.
Where it is desired only that such a cylindrical Array be omnidirectional in the plane perpendicular to the cylinder axis, considerable savings on transducer drive amplifiers and signal processing electronics may be achieved by driving all transducers at the same (or nearly the same) position along the cylinder axis (irrespective of their angular position around said axis) with one and the same electrical drive signal produced by just one drive amplifier and signal processing channel. E.g. for a professional-audio Array with cylinder diameter of 1.1 m and 100 mm diameter 10 watt rated transducers, approximately 32 transducers may be positioned around each circumferential ring of the cylinder. Thus for a horizontally omnidirectional (only) Array (assuming the cylinder is mounted with axis vertical) just one 320W amplifier plus one signal processing channel could be used to drive the whole ring, a great saving in cost and complexity (eliminates 31 power amplifiers and signal processing chains, and associated wiring and connectors), especially as the cost of power amplifiers is only a weak function of their power rating in this region. Note that total flexibility of beam forming and steering in the direction parallel to the cylinder axis is still retained under this scheme, and in general conical-shell beams may be produced with any cone angle. Partial use of this idea may also be made resulting still in considerable cost savings; e.g. each semicircle or quadrant (or third, fifth, octant etc) of transducers of each circumferential ring could be driven with a power amplifier, resulting in elimination of 30 or 28 amplifiers and signal processing chains respectively.
In another variant of cylindrical arrays of the first aspect of the invention, transducers in regions on opposite sides of the (or an) axis of symmetry of the Array (e.g. the axis of the cylinder for a cylindrical array, or a diameter for a spherical array) may be driven in antiphase with optional relative drive power weighting. Consider for example the case where every other ring of transducers around the cylinder axis is driven totally in-phase, with the rings in-between these driven as two antiphase semicircles of transducers (with the separating diameters of all the antiphase rings aligned). Then the array behaves like a stack of dipole radiators alternating with monopole radiators, and the resulting overall response will be the classic cardioid polar distribution, with strong radiation in one direction and a complete null in the opposite direction. Variations on this simple arrangement abound, but an immediate possibility that arises with the 2D/3D Array implementation as described, of this cardioid radiator, is that the direction of maximum radiation can be altered at will by simple signal processing means (i.e. by selecting which subsets of transducers in each ring form the semicircular phase-opposed rings), thus enabling rapid and flexible beam sweeping or rotating, and in some applications, even more importantly, null-direction sweeping or rotating. The advantage of making a cardioid Array in this manner is that because of the large number of transducers (and the fine tuning available with the signal processing in phase/delay and amplitude) very accurately matched monopole and dipole sources may be synthesised thus giving a very sharp null to the radiation pattern.
The possibilities described above for a cylindrical Array design of the invention, may be carried over to the case where instead of cylindrical, the Array is made conical, or spherical. Where there is a well defined preferred latitude angle of radiation from the Array in a given application, there can be advantages (primarily in making best use of the radiation pattern of individual transducers at high frequencies) in using a conical rather than cylindrical array, with the cone angle such that the sloping sides of the cone are normal to that preferred latitude angle. Otherwise, the use considerations are essentially the same as for the cylindrical array previously described.
Where a spherical 2D surface array is used (transducers now being approximately uniformly distributed over the surface of a sphere) further advantages arise. Just as the cylindrical Array allows uniform beam coverage in 2 pi rads of one plane, use of a spherical Array allows 4 pi steradian coverage in 3-space, with beams freely being generated in any conceivable direction from the centre of the Array, and in particular, simultaneous beams in any 2 or more completely independent directions including opposite directions. This is impossible with conventional loudspeakers, and indeed with prior art planar Arrays. Applications for such true 3D capable beam forming arrays are particularly to be found in very large buildings (such as auditoria, concert halls (e.g. Royal Albert Hall), very large atrium structures, and underwater).
In another co-owned published international patent application (WO03/034780) are described reasons and techniques for using a non-uniform distribution of transducers over the surface of a planar Array. It should be noted that these reasons and techniques carry over to highly curved non-planar Arrays of the present invention, suitably adjusted for the new geometry, and in certain applications technical advantages may be achieved by use of such non-uniform transducer distributions (primarily the advantages are reduction of grating sidelobe amplitudes at the expense of some primary beam broadening), and it is intended that non-uniform transducer distribution variants of all of the geometric forms of Arrays described in the present invention should also form part of the present invention, as will be evident to those skilled in the art.
A second aspect of the invention provides apparatus for creating a sound field, said apparatus comprising: an array of sonic output transducers, which array is capable of directing at least one beam in a first selected direction; wherein said transducers lie on a curved surface; and wherein said apparatus comprises a processor arranged to determine a first subset of transducers to use when directing sound in said first direction.
There is also provided a method for creating a sound field, said method comprising: providing an array of sonic output transducers which lie on a curved surface; selecting a direction in which to beam sound; selecting a first subset of transducers in accordance with said direction such that said first subset contains only those transducers that have an unimpeded component of radiation in a direction which contributes to a beam in said selected direction; using only said first subset of transducers to beam sound in said selected direction.
In another aspect of the invention, Arrays of any 3D shape are volume-populated with array transducers—i.e. rather than simply covering the surface of a 3D volume (e.g. a cylinder, cone or sphere) with transducers, the space within the volume also contains transducers, and there is no “surface” as such. Indeed, as much as possible of the space surrounding each of the transducers should preferably be kept clear of solid materials (or other sound absorbing, reflecting or refracting substance) so as to minimally impede the acoustic radiation from each transducer. Transducers within such true 3D Arrays should preferably be 3D omnidirectional, and preferably monopole rather than dipole radiators, which implies that they either need to be small compared to a wavelength of sound at frequencies of interest, or, they should be of approximately spherically symmetric construction, at least at their radiating surface. Such a true 3D Array combines the directivity effects of both conventional planar Arrays (and highly curved Arrays of the first aspect of the present invention) with the directivity of end-fire arrays (end-fire arrays have significant extent compared to a wavelength in the direction of beaming, whereas planar arrays have significant extent at right angles to the direction of beaming). A 3D Array of the present invention combines the potentially full 4 pi steradian beam radiation characteristic of the previously described spherical highly curved Array, with the additional directivity achieved by simultaneous use of end-fire Array beaming. A practical 3D Array structure might usefully have the transducers mechanically connected by an open thin rod lattice of support members (each support member being effectively acoustically invisible by dint of its small cross section) thus forming a rigid overall structure without any sound-blocking panels or large surfaces other than the transducers themselves. The transducers will preferably be small in extent compared to wavelengths of interest so as to minimally affect the passage of sound energy from surrounding transducers by reflection, refraction and diffraction. The per transducer delays are calculated in a similar manner, for a given desired beam shape, as per prior art Arrays and first aspect invention Arrays; i.e. the delays are chosen such that radiation from each transducer arrives at the Focal Point simultaneously, taking into account their individual 3D coordinates. In this case however, unlike with the Arrays of the first aspect of the invention, it is not necessary to calculate which transducers to recruit for the production of a beam in any particular direction, as all transducers may equally participate, as there is no transducer shadowing, as there is no structure to throw (acoustic) shadows, other than the transducers themselves and their deliberately minimal support structures. Of course it is optionally possible to select out certain transducers for other reasons, but in general the situation is now physically different from previously known arrays and there are specific advantages in using all of the transducers in the Array for beams in all directions, specifically, increased directivity and increased beam power. These are considerable advantages, especially when taken together with the simplification of beam computations (i.e. no need to compute transducer inclusion/exclusion, even when sweeping beam directions in 2D or 3D).
Applications for such true 3D Arrays are all those for other Array types, plus new applications where the true 3D beam direction (over 4 pi steradians) capabilities are advantageous, and also where an Array of smaller maximum extent but increased directivity and/or radiated power are beneficial (due to the combination of lateral and end-fire directivity characteristics).
The nature of Arrays being that with suitable replacement of transducer drive amplifiers with sensitive receive amplifiers, and replacement of transmission transducers (e.g. loudspeakers) with reception transducers (e.g. microphones), and with suitable modification of the arrangement of the signal processing equipment and summing junctions (all of which is known in the prior art) one may use a similar transmission Array geometric structure as a reception array. This reciprocal behaviour also applies to all of the Arrays of the present invention and it is to be understood that everything that is said here relating to transmission Array loudspeakers, may equally be applied to reception Array microphone systems, and it is intended that such microphone variants are to be included in the present invention.
Preferably, a processor is used to weight the signals routed to each transducer so as to reduce unwanted beams in the sound field. Such waiting is preferably performed in accordance with a windowing function. Preferred windowing functions are sinc functions, cosinusoidal functions and DC offset values. Combinations of these three functions may also be used to achieve the optimum result.
The invention will now be further explained, by way of example only, with reference to the accompanying drawings, in which:
These drawings and the ideas embodied in them will now be explained in greater detail.
Suitable windowing (apodization) techniques applicable to non-planar arrays will now be discussed. Consider a practical cylindrical 3D DDAA wherein a truncated cylindrical form of diameter D and height H, has its surface covered with elements in a regular triangular grid pattern, over all 360deg around the cylinder and over the entire extent H of the cylinder's height. Such a device is sketched in
There are 3 cases to be examined.
Case 1: Here the wavelength L of the radiation is small compared with the cylinder diameter D, i.e. L<<D;
Case 2: Here the wavelength L of the radiation is similar to the cylinder diameter D, i.e. L˜D;
Case 3: Here the wavelength L of the radiation is large compared with the cylinder diameter D, i.e. L>>D;
For the purposes of discussion we will consider only the transmission array case, used for acoustic waves, but it will be evident to those versed in the art that similar principles apply to the receiving antenna case, and to other wave types than acoustic (with suitable change of wave velocity etc).
We also make the assumption that the array elements are nominally all of the same diameter d, and are hemi-omnidirectional (i.e. radiate approximately equally in all directions outside a tangent plane to the cylinder passing through each element's centre point) over their useful working frequency range, and fully omnidirectional at lower frequencies where the wavelength is very much greater than their diameter d, again without loss of generality.
In Case 1, L<<D. Consider a requirement to form a radiated sound beam from the 3D DDAA (hereinafter just called the cylinder) in a given direction theta relative to some axes fixed in the centre of the cylinder, and we consider without loss of generality (but with less detail required) only the case where the beam is to be radiated in the direction orthogonal to the central axis of the cylinder. Then, all of the array elements in the hemi-cylinder centred on direction theta have line of sight to the beam direction (the ones at the edge of this hemi-cylinder are marginally so) and all may contribute usefully to the beam. One computes their respective delays in order to form such a beam in the usual way for DDAAs taking into account not just their distance across the array but also their 3D coordinates (i.e. their varying distance from a plane orthogonal to the beam direction), as these will now vary considerably as the array is cylindrical, not planar.
The remainder of the transducers (in the opposite hemi-cylinder) cannot usefully contribute to the beam, as the cylinder itself effectively blocks their radiation, because L<<D. So using an un-apodized array will clearly produce unwanted radiation, a spurious beam of some kind, in a direction opposite to the desired beam direction, as all of these latter transducers are effectively isolated from the ones in the other hemi-cylinder by the physical structure of the cylinder, and so no destructive interference on the far side of the cylinder from the beam can take place (utilising the radiation from elements on the near side to the beam) as would normally occur in a DDAA. This is a new problem, arising from the 3D nature of the DDAA structure.
This situation is depicted in
It is a purpose of the present invention to eliminate or at least reduce this problem, i.e. the unwanted spurious beam. We find by analysis and experiment that the spurious beam may be greatly diminished in Case 1 by using an apodization function of the following form:
First, as we are only considering for simplicity beams in a plane orthogonal to the cylinder axis, the apodization function will be constant along the surface of the cylinder in a direction orthogonal to this plane (i.e. constant up and down the length of the cylinder), although in practice this direction may be usefully weighted with the usual candidate functions such as raised cosine etc to taper the array in the length-of-cylinder direction to minimise sidelobes in this direction. So we will only further consider the shape of the apodization function in the plane around the cylinder axis.
Second, we find that apodization functions that are approximately or actually symmetrical in this latter plane about the beam direction are most effective.
Thirdly, we find that apodization functions which are of the following form are very effective:
Of course, there are very many such oscillatory functions that may be used to good effect.
The point to notice is that we are using the sine function weighting here in a new situation, the 3D DDAA, and to achieve a different purpose than previously—i.e. to minimize unwanted beams due to the blocking effect of the physical structure of the 3D DDAA itself, rather than to simply achieve a modified (e.g. flatter) beam pattern as is the case when sinc functions are used in planar DDAAs.
In addition to characteristics a) to e) above, we also find that useful additional features may be added to the apodization function as follows:
Case 2 requires a transitional, intermediate apodization function, between that for Case 1 (e.g. a sinc function) and that for Case 3 (a flat apodization function).
When the cylinder height H is large compared with a wavelength (H>>L) then in the direction of the cylinder axis it is desirable to apply either a uniform apodization function (for maximum radiation sensitivity and beam sharpness, but with larger sidelobes in this direction, or one of the conventional apodizations such as raised cosine.
For a spherical or ellipsoidal DDAA the results just described for the cylindrical DDAA for the plane orthogonal to the cylinder axis, may be applied also to the orthogonal direction, so that for example, an apodization function in the form of, e.g. a 2D sinc function centred on the desired beam direction, will work well for the case D>>L; and again surprisingly for the converse case where D<<L a uniform apodization function over the entire spherical/ellipsoidal array will work well in the sense of minimising unwanted rear-direction beams.
| Number | Date | Country | Kind |
|---|---|---|---|
| 0417712.7 | Aug 2004 | GB | national |
| 0501879.1 | Jan 2005 | GB | national |
| Filing Document | Filing Date | Country | Kind | 371c Date |
|---|---|---|---|---|
| PCT/GB05/03140 | 8/10/2005 | WO | 2/9/2007 |
